Calculate investment's interest rate to break-even insurance cost [duplicate]
I believe the following formula provides a reasonable approximation. You need to fill in the following variables: The average annual return you need on investing the 15% =  (((MP5 - MP20) * 12) + (.0326 * .95 * PP / Y)) / (PP *.15) Example assuming an interest rate of 4% on a 100K home: If you invest the $15K you'll break even if you make a 9.86% return per year on average. Here's the breakdown per year using these example numbers: Note this does not consider taxes. You are comparing a risk-free cost with a risky return. If you can tolerate that level of risk (the ups and downs of the investment) for the chance that you'll come out ahead in the long-run, then sure, you could do that.   So the parameters to your equation would be: If you assume that the risky returns are normally distributed, then you can use normal probability tables to determine what risk level you can tolerate. To put some real numbers to it, take the average S&P 500 return of 10% and standard deviation of 18%.  Using standard normal functions, we can calculate the probability that you earn more than various interest rates: so even with a low 3% interest rate, there's roughly a 1 in 3 chance that you'll actually be worse off (the gains on your investments will be less than the interest you pay).  In any case there's a 3 in 10 chance that your investments will lose money. I wouldn't call it apples and oranges.  This is literally an opportunity cost calculation.  You can safely assume S&P500 will perform at least 11% over any 10 year period.  Since failing companies are delisted and replaced with new growing companies, the market should continue to grow.  No, it's not guaranteed.  Lets use an aggressive number for inflation, 4%, leaving a 7% ROR estimate for S&P500.  I assume OP has better credit than me, assume a rate around 3.5%.  So it looks like net 3.5% ROR.  The PMI erases that.  You have to continue paying it until you pay off the loan.   Put 20% down, get a 15 year fixed at lowest rate.  Pay it off quicker.
Yes - it's called the rate of inflation. The rate of return over the rate of inflation is called the real rate of return.   So if a currency experiences a 2% rate of inflation, and your investment makes a 3% rate of return, your real rate of return is only 1%. One problem is that inflation is always backwards-looking, while investment returns are always forward-looking. There are ways to calculate an expected rate of inflation from foreign exchange futures and other market instruments, though. That said, when comparing investments, typically all investments are in the same currency, so the effect of inflation is the same, and inflation makes  no difference in a comparative analysis.  When comparing investments in different currencies, then the rate of inflation may become important. "The question that I walk away with is ""What is the cost of the downside protection?"" Disclaimer - I don't sell anything. I am not a fan of insurance as an investment, with rare exceptions. (I'll stop there, all else is a tangent) There's an appeal to looking at the distribution of stock returns. It looks a bit like a bell curve, with a median at 10% or so, and a standard deviation of 15 or so. This implies that there are some number of years on average that the market will be down, and others, about 2/3, up. Now, you wish to purchase a way of avoiding that negative return, and need to ask yourself what it's worth to do so.  The insurance company tells you (a) 2% off the top, i.e. no dividends and (b) we will clip the high end, over 9.5%.  I then am compelled to look at the numbers. Knowing that your product can't be bought and sold every year, it's appropriate to look at 10-yr rolling returns. The annual returns I see, and the return you'd have in any period. I start with 1900-2012. I see an average 9.8% with STD of 5.3%. Remember, the 10 year rolling will do a good job pushing the STD down. The return the Insurance would give you is an average 5.4%, with STD of .01. You've bought your way out of all risk, but at what cost?  From 1900-2012, my dollar grows to $30080, yours, to $406. For much of the time, treasuries were higher than your return. Much higher.  It's interesting to see how often the market is over 10% for the year, clip too many of those and you really lose out.  From 1900-2012, I count 31 negative years (ouch) but 64 years over 9.5%. The 31 averaged -13.5%, the 64, 25.3%.  The illusion of ""market gains"" is how this product is sold. Long term, they lag safe treasuries." R = I ^ P R = return (2 means double)  I = (Intrest rate / 100) + 1 [1.104 = 10.4%] P = number of periods (7 years)  2 = 1.104 ^ 7 (you double your money in seven years with a yearly Intrest rate of 10.4%) I = R^(1/P) 1.104 = 2^(1/7) P = log(R) / log(I)  7 = log(2) / log(1.104) This calculation arrives at the correct answer.  However, it uses the formula for an annuity due.  This means the payments are made at the beginning of the month and the last month of the 10 year period has interest accrued. See the section, Calculating the Future Value of an Annuity Due. The rate is given as an effective rate. with  In Excel, =FV((1+0.12)^(1/12)-1,120,3500,0,1) The total number of shares on April 1st is 100 + 180 + 275 = 555.  The price on April 1st is required.  The current price is stated as $2, but $2 * 555 = $1110 and the current fund values is stated as $1500.  Opting to take the current value as $1500, the price on April 1st can be calculated as $1500/555 = $2.7027. The amounts invested as number of shares x share price are: (Note these investment amounts do not match the example scenario's investment amounts, presumably because the example numbers are just made up.) The monthly returns can be calculated: The current values for each investor as invested amount x returns are: Checking the total: "Hello! I am working on a project where I am trying to determine the profit made by a vendor if they hold our funds for 5 days in order to collect the interest on those funds during that period before paying a third party.  Currently I am doing ""Amount x(Fed Funds Rate/365)x5"" but my output seems too low. Any advice?" Calculate the theoretical forward price using covered interest parity, then compare it to the actual forward price of $1.04/euro. Buy the cheap one and sell the expensive one (this will involve borrowing dollars or euros at the US or Euro interest rate to buy the other currency and longing or shorting the 6-month forward to perfectly hedge your currency exposure). These are the steps I'd follow: $200 today times (1.04)^10 = Cost in year 10.  The 6 deposits of $20 will be one time value calculation with a resulting year 7 final value. You then must apply 10% for 3 years (1.1)^3 to get the 10th year result.  You now have the shortfall. Divide that by the same (1.1)^3 to shift the present value to start of year 7. (this step might confuse you?) You are left with a problem needing 3 same deposits, a known rate, and desired FV. Solve from there.  (Also, welcome from quant.SE. This site doesn't support LATEX, so I edited the image above.) This investment does not have a payback period as the net present value of your investment is negative. Your investment requires an initial cash outlay of $40,000 followed by annual savings of $2060 for the next 20 years. Your discount rate is 5% at which the NPV is $-14327.85 as calculated below by using this JavaScript financial functions library tadJS that is based on a popular tadXL add-in for Excel 2007, 2010 and 2013. "Hey guys I have a quick question about a financial accounting problem although I think it's not really an ""accounting"" problem but just a bond problem.  Here it goes    GSB Corporation issued semiannual coupon bonds with a face value of $110,000 several years ago. The annual coupon rate is 8%, with two coupons due each year, six months apart. The historical market interest rate was 10% compounded semiannually when GSB Corporation issued the bonds, equal to an effective interest rate of 10.25% [= (1.05 × 1.05) – 1]. GSB Corporation accounts for these bonds using amortized cost measurement based on the historical market interest rate. The current market interest rate at the beginning of the current year on these bonds was 6% compounded semiannually, for an effective interest rate of 6.09% [= (1.03 × 1.03) – 1]. The market interest rate remained at this level throughout the current year. The bonds had a book value of $100,000 at the beginning of the current year. When the firm made the payment at the end of the first six months of the current year, the accountant debited a liability for the exact amount of cash paid. Compute the amount of interest expense on these bonds for the last six months of the life of the bonds, assuming all bonds remain outstanding until the retirement date.  My question is why would they give me the effective interest rate for both the historical and current rate?  The problem states that the firm accounts for the bond using historical interest which is 10% semiannual and the coupon payments are 4400 twice per year.  I was just wondering if I should just do the (Beginning Balance (which is 100000 in this case) x 1.05)-4400=Ending Balance so on and so forth until I get to the 110000 maturity value. I got an answer of 5474.97 and was wondering if that's the correct approach or not." I asked this question in another sub, but I thought I might also get answers here.   I was just wondering how pension funds or investment firms calculate the interest that they give to their members or clients in the US, or whichever country you are from.   I ask this because I have a gut feeling that the national pension fund in my country does it the wrong way and is basically cheating people, so I wanted to make a comparison with other countries. Forgive me if I'm wrong and there's nothing to worry about.   OK, so what they do is collect money in a given financial year, which starts in July and ends in June. Let's say they collect 100 million in 2010-11. They then invest this 100 million in the year July 2011 - June 2012. After deducting admin costs and all that, interest for this 2010-11 money is declared on October 1st 2012.   That basically means that money someone contributed in July 2010 will earn interest 2 years later in 2012! I just feel like that is not how it should be done, but you can correct me if I'm wrong.   They also regularly give interest at about 12% which is good when I read about interest rates in the US being around 7%, but I feel like since this interest is basically announced after 2 years, that 12% isn't as good as it seems.   Someone help me understand if I'm wrong.  Thanks. Im creating a 5-year projection on Profit and loss, cash flow and balance sheet and i\m suppose to use the LIBOR (5 year forward curve) as interest rate on debt.  This is the information i am given and it in USD.  Thanks for the link.  I guess its the USD LIBOR today, in one year, in two years, three years, four years and five years For this, the internal rate of return is preferred. In short, all cash flows need to be discounted to the present and set equal to 0 so that an implied rate of return can be calculated. You could try to work this out by hand, but it's practically hopeless because of solving for roots of the implied rate of return which are most likely complex. It's better to use a spreadsheet with this capability such as OpenOffice's Calc. The average return on equity is 9%, so anything higher than that is a rational choice. Example Using this simple tool, the formula variables can easily be input. For instance, the first year has a presumed cash inflow of $2,460 because the insurance has a 30% discount from $8,200 that is assumed to be otherwise paid, a cash inflow of $40,000 to finance the sprinklers, a cash outflow of $40,000 to fund the sprinklers, a $400 outflow for inspection, and an outflow in the amount of the first year's interest on the loan. This should be repeated for each year.  They can be input undiscounted, as they are, for each year, and the calculator will do the rest. "The answer to almost all questions of this type is to draw a diagram.  This will show you in graphical fashion the timing of all payments out and payments received.  Then, if all these payments are brought to the same date and set equal to each other (using the desired rate of return), the equation to be solved is generated. In this case, taking the start of the bond's life as the point of reference, the various amounts are: Pay out = X Received = a series of 15 annual payments of $70, the first coming in 1 year.  This can be brought to the reference date using the formula for the present value of an ordinary annuity. PLUS Received = A single payment of $1000, made 15 years in the future.  This can be brought to the reference date using the simple interest formula. Set the pay-out equal to the present value of the payments received and solve for X I am unaware of the difference, if any, between ""current rate"" and ""rate to maturity"" Finding the rate for such a series of payments would start out the same as above, but solving the resulting equation for the interest rate would be a daunting task..." If I is the initial deposit, P the periodic deposit, r the rent per period, n the number of periods, and F the final value, than we can combine two formulas into one to get the following answer: F = I*(1+r)n + P*[(1+r)n-1]/r In this case, you get V = 1000*(1.05)20 + 100*[(1.05)20-1]/0.05 = 5959.89 USD. Note that the actual final value may be lower because of rounding errors.