Question

Nakiri invests $8,000 at age 18. She hopes the investment will be worth $64,000 when she turns 35. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.

Answer 1

12.2%

Explanation:

Answer 2

Rate of interest is 12.232%, if Nakiri invests $8,000 at age 18 and she hopes the investment will be worth $64,000 when she turns 35.

Explanation:

The given is,

Investment amount $8000 at age of 18

Future worth $64000 at age of 35

Step:1

Formula to calculate the future amount with an interest of compounded continuously,

`F= Pe^(rt)`..........................(1)

Where,

F - Future amount

P - Present amount

r - Rate of interest

t - No.of years

Constant, e = 2.7183

From given,

P = $8000

F = $64000

t = 35-18 = 17 years

Equation (1) becomes,

`64000= 8000 (2.7183)^((r)(17) )`

`(64000)/(8000) = 2.7183^((r)(17))`

`8 = 2.7183^((r)(17))`

Take log on both sides,

`log 8 = (r)(17)log 2.7183`

Substitute log values of 8 and 2.7183

0.90308999 = ( r × 17 ) (0.4342974)

`(0.90308999)/(0.4342974) = (r)(17)`

2.07942 = ( r × 17 )

`r=(2.0794275)/(17)`

r = 12.232

Result:

Rate of interest is 12.232%, if Nakiri invests $8,000 at age 18 and she hopes the investment will be worth $64,000 when she turns 35.