Question

1.)  Suppose a person invests $2000 per year (at the end of each year) in a retirement account. The value of the account depends on the invest rate being paid and the number of years for which contributions are made. To investigate this, calculate the future value of such an account after 15,20,25 and 30 years using an annual interest rate of 4%, 6%, 8% and 12%. organize the results in a table and show your calculations.

2.) a) Describe the effects on the future value of changing the following (cite examples)

i) the number of years while keeping everything else fixed,

ii) the interest rate while keeping everything else fixed,

  b) Which has a bigger effect on the future value, doubling the the time from 15 to 30 years or doubling the interest rate from 4% to 8%? (cite examples)

3) In this question assume the interest rate stays at 6%

  a) What effect would doubling the contribution(to $4000 per year) have on the future value of the account (if everything else is kept fixed) ?

  b)Is the effect larger or smaller than the effect of doubling the time from 15 years to 30 years( while keeping everything else fixed)

4)  Based on your answers 1-3, which variable has the largest effect on the future value of a retirement account: time over which contributions are made, interest rate, or contribution amount?

Answer 1

future value
year/rate	4%	6%	8%	12%
15	40,047.18	46,551.94	54,304.23	74,559.43
20	59,556.16	73,571.18	91,523.93	144,104.88
25	83,291.82	109,729.02	146,211.88	266,667.74
30	112,169.88	158,116.37	226,566.42	482,665.37

we can clearly conclude that that as the interest rate increased the future value is increased

similarly as the no of year of investment is increased the future value is also increased.

year/rate	0.04	0.06	0.08	0.12
15	=-FV(4%,15,2000,0)	=-FV(6%,15,2000,0)	=-FV(8%,15,2000,0)	=-FV(12%,15,2000,0)
20	=-FV(4%,20,2000,0)	=-FV(6%,20,2000,0)	=-FV(8%,20,2000,0)	=-FV(12%,20,2000,0)
25	=-FV(4%,25,2000,0)	=-FV(6%,25,2000,0)	=-FV(8%,25,2000,0)	=-FV(12%,25,2000,0)
30	=-FV(4%,30,2000,0)	=-FV(6%,30,2000,0)	=-FV(8%,30,2000,0)	=-FV(12%,30,2000,0)