Question

Assume you make the following​ investments:

a.	You invest a lump sum of $7,550 for five years at 12​% interest. What is the​ investment's value at the end of fivefive ​years?
b.	In a different account earning 1212​% ​interest, you invest $1,510 at the end of each year for fivefive years. What is the​ investment's value at the end of fivefive ​years?
c.	What general rule of thumb explains the difference in the​ investments' future​ values?

Answer 1

a. Future Value = Present Value (1 + Periodic Interest Rate)^ Period

Future Value = 7550 * (1 + 0.12)^5

= 7550*(1.12)^5

= 7550*1.762342 = $ 13305.68

b. Future Value = Instalment * Future Value interest factor annuity

= 1510 * 6.3528 = $ 9592.728

c. Though the amount of investment made is same under both the alternatives, the difference in the future values is due to the difference in the timing of investment made. In case A, the amount is invested at one time initially, the interest accumulates on the whole amount for 5 years.While for the Case B, the amount is invested at different time periods, hence the interest amount would be low.