Question

You invest $5,000 in the stock market today and you expect a return of 7% annually. What do you expect this investment to be worth in 20 years? How many years will it take for this investment to double in value? Recalculate your answers with a return of 7% quarterly. Describe how the investment grows over time using terminology.

Answer 1

Answer 1)

This investment will be worth 19,348.42 in 20 years if we expect to earn 7% annually,

Present Value	5000
Interest	7%
Time Period (N)	20

Future Value = Present Value * (1+int%)^N

FV = 5000 * (1.07)^20

FV = 19,348.42

Answer 2)

Present Value	5000
Interest	7%
Future Value (PV *2)	10,000

Using Financial Calculator and using the following steps to calculate the time period to double in value:

1) Insert -5000 and press PV (negative since investing money i.e. outflow of cash)

2) Insert 10,000 and press FV

3) Insert 7% and press I/Y

4) Insert 0 and press PMT (No annual payments)

5) Press CPT and Press N.

We get time period = 10.24 years

Answer 3)

Recalculating Future value with 7% quarterly in Answer 1.

Future Value = Present Value * (1+int%/4)^(N*4)

Multiply N with 4 and divide int% with 4 due to quarterly periods

N = 20 * 4 = 80

Int % = 7% /4 = 1.75%

Future Value = 5000 * (1.0175)^80

Future Value = 20,031.96

Recalculating Time period with 7% quarterly in Answer 2

Present Value	5000
Interest (7%/4)	1.75%
Future Value (PV *2)	10,000

Using Financial Calculator and using the following steps to calculate the time period to double in value:

1) Insert -5000 and press PV (negative since investing money i.e. outflow of cash)

2) Insert 10,000 and press FV

3) Insert 1.75% and press I/Y

4) Insert 0 and press PMT (No annual payments)

5) Press CPT and Press N.

We get time period = 39.95 quarters.

Answer 4)

The future value is the value of an investment at a future date as it grows over time at a specific rate of return.The future value is important to determine how much the investment today is worth after n years. It enables investors to make sound investment decisions and financial planning.

Future Value = Investment * (1 + int%) ^N