Question

1) How much will you have accumulated over a period of 35 years if, in an IRA which has a 10% interest rate compounded monthly, you annually invest:

a. $1

b. $5000

c. $8,000

d. Part (a) is called the effective yield of an account. How could Part (a) be used to determine Parts (b) and (c)?

(Your answer should be in complete sentences)

Answer 1

a) Assuming, month $1/12 is invested at an interest rate of 10% compounded monthly, future value of this investment accumulated over 35 years can be calculated in excel with the formula FV(Rate,Nper,Pmt)

Here, Rate = Monthly Interest Rate = 10%/12 = 0.833%

Nper = Period in Months = 35*12 = 420

Pmt = Monthly Contribution = $1/12 = 0.0833

With these inputs, FV(0.833%,420,0.833) = 316.3865

b) If Annual Investment = $5,000, then Pmt = Monthly Contribution = $5000/12 = 416.667

Here, accumulated value of investment = FV(0.833%,420,416.667) = $ 1,581,932.52

c) If Annual Investment = $8,000, then Pmt = Monthly Contribution = $8000/12 = 666.667

Here, accumulated value of investment = FV(0.833%,420,666.667) = $ 2,531,092.03

d) With effective yield calculated in (a), accumulated value of investment of part (b) & part (c) can be calculated as annual investment * effective yield. That is, for (b), accumulated value of investment = $5000 * 316.3865 = $ 1,581,932.52. Similarly, for (c), accumulated value of investment = $8000 * 316.3865 = $ 2,531,092.03