Help on a compound interest question?

Here's the question: You made a registered retirement savings plan deposit of $1000 on December 1, 2008 at a fixed rate of 5.5% compounded monthly. If you withdraw the deposit on August 1, 2015, how much will you receive? Can someone give me step-by-step instructions on how I solve this with a business calculator (BA II Plus)? Thanks in advance.

Public Comments

1. P=C(1+r/n)^nt P=1000(1+0.05/12)^[12*(2015-2008)] P=1000(1.004)^84 P=1000(1.418) P=$1418.04
2. First, recall the formula A(t) = A(0)*(1+i/n)^(nt), where: A(t) = accumulated/future value at end of period t A(0) = accumulated/future value at time 0, or amount of initial deposit i = NOMINAL annual interest rate n = number of times that NOMINAL annual interest rate is compounded per year In the BA II Plus, this formula becomes FV = PV*[1+(I/Y)/100]^N, where: FV = accumulated value/future value PV = deposit (opposite sign from FV) I/Y = EFFECTIVE periodic interest rate as a percent, not a decimal (so, to enter 5%, type 5, not .05) N = number of compounding periods that deposit is accumulated over 1. I always set P/Y and C/Y to 1 to make things easier. To set this, hit 2nd, then I/Y, then use the arrows to make sure that P/Y and C/Y are set to 1. 2. There are 6 years from December 1, 2008 to December 1, 2014. This is equivalent to 6*12 = 72 months. Then, there are 8 more months to get from December 1, 2014 to August 1, 2015. Therefore, there are 80 months from December 1, 2008 to August 1, 2015. Therefore, there are 80 interest compounding periods, or N=80. So in your calculator, type 80, followed by N. 3. The NOMINAL interest rate is 5.5% compounded monthly. Therefore, the EFFECTIVE monthly interest rate is 5.5% / 12 = (5.5 / 12) %. So, type 5.5 divided by 12 = I/Y. Note that N and I/Y are assumed by the calculator to be over the same period. That's why we made N the number of months and I/Y the effective monthly interest rate. (later, when you cover annuities and bonds, you'll need to make sure that all 5 keys are using the same period) 4. Then type 1000 +/- PV, since 1000 is the deposit. 5. Finally, type CPT FV to compute the accumulated/future value of the $1000 deposit (This should be 1441.7086 if you have your calculator formatted to display 4 decimal places). Note that the BA II Plus uses different signs for cash inflows and cash outflows. You put $1000 INTO the fund on December 1, 2008, and you get $1441.71 OUT OF the fund on August 1, 2015. That's why the PV and FV have opposite signs. You could have entered PV as a positive number, in which case the FV would be output as negative.