Mathematics, 11.04.2020 18:16 sssssaaaaaddddd5712

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.

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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.

Step-by-step 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,

$64000= 8000 (2.7183)^{(r)(17) }$

$\frac{64000}{8000} = 2.7183^{(r)(17)}$

$8 = 2.7183^{(r)(17)}$

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)

$\frac{0.90308999}{0.4342974} = (r)(17)$

2.07942 = ( r × 17 )

$r=\frac{2.0794275}{17}$

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.

Answer from: Quest

312312

step-by-step explanation:

Answer from: Quest

32.10 is the correct answer

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Nakiri invests $8,000 at age 18. She hopes the investment will be worth $64,000 when she turns 35. I...