Chapter 5, Problem 1DTM

Invest Now or Later? Twins Natalie and Kaitlyn are both age 27. They both live in Warren, Ohio. Beginning at age 27, Natalie invests $2,000 per year for ten years and then never sets aside another penny. Kaitlyn waits ten years and then invests $2,000 per year for the next 30 years. Assuming they both earn 7 percent, how much will each twin have at age 67? (Hint: Use Appendixes A.1 and A.3 or visit the Garman/Forgue companion website.

Summary Introduction

To calculate:The future value of the investment of each person.

Introduction: Time value of money is the concept of finance which calculates the effect of time over the value of money. As per this concept the present value of a future amount is lower than the future value. The present value/ future value of an amount is calculated using the interest rate as discount rate.

Answer to Problem 1DTM

The future value of the investment of each person is as follows:

	Future value of investment
N	$ 2,10,350.68
K	$ 7,31,069.92

Explanation of Solution

The future value of the investment of each person is calculated as follows:

N:
Annual investment (A)	$ 2,000
Years of investment (B)	10
Interest rate (C)	7%
Future value of annuity $1 (7%, 10 years) (D)	13.8165
Future value after 10 years (E) (A   $\times$ D)	$ 27,633
Remaining years (F) (67-37)	30
Future value of lump sum $1 (7%, 30 years) (G)	7.6123
Future value at the age of 67 (E   $\times$ G))	$ 2,10,350.68
K:
Annual investment (A)	$ 2,000
Years of investment (B)	30
Interest rate (C)	7%
Future value of annuity $1 (7%, 30 years) (D)	94.4608
Future value after 30 years (E) (A $\times$ D)	$ 1,88,921.60
Remaining years (F) (67-47)	20
Future value of lump sum $1 (7%, 20 years) (G)	3.8697
Future value at the age of 67 (E $\times$G))	$ 7,31,069.92