Use the compound interest formula , where P is the original amount of the investment, i is the interest rate per compounded period, n is the total number of compounding periods, and A is the value of the investment after n periods. To save for post-secondary tuition, a parent invests $8000 in a mutual fund that earns interest at the rate of 5.9% per year compounded monthly.
In approximately how many years will the investment be worth $13,700? Round to the nearest year.
A) 8 years
B) 4 years
C) 14 years
D) 9 years

Question

Use the compound interest formula  , where P is the original amount of the investment, i is the interest rate per compounded period, n is the total number of compounding periods, and A is the value of the investment after n periods. To save for post-secondary tuition, a parent invests $8000 in a mutual fund that earns interest at the rate of 5.9% per year compounded monthly.
In approximately how many years will the investment be worth $13,700? Round to the nearest year.
A) 8 years 
B) 4 years 
C) 14 years 
D) 9 years

Quizplus · Accepted Answer

Using the compound interest formula:

A = P(1 + i)^n

where 
P = $8000 
i = 5.9% / 12 (monthly rate) = 0.004917 
A = $13,700

Plugging in the values:

$13,700 = $8000(1 + 0.004917)^n

Dividing both sides by $8000 and taking the logarithm of both sides:

log(1.7125) / log(1.004917) = n

n ≈ 9

Therefore, it will take approximately 9 years for the investment to be worth $13,700. Rounded to the nearest year, the answer is D) 9 years.

Use the Compound Interest Formula , Where P Is