Question

Jake earned $9,136.00 from a summer job and put it in a savings account that earns 11% interest compounded quarterly when Jake started college he had $14,942.00 in the account which he used to pay for tuition. how long was the money in the account

Answer 1

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=9,136.00

A=14,942.00

r=11%=11/100=0.11

n=4

substitute in the formula above

`\begin{gathered} 14,942=9,136(1+(0.11)/(4))^(4t) \\ (14,942)/(9,136)=(((4.11)/(4))^4)^t \\ \\ \text{Apply log both sides} \\ \log ((14,942)/(9,136))=t\cdot\log ((4.11)/(4))^4 \\ \text{solve for t} \\ t=\log ((14,942)/(9,136))\text{ : }\cdot\log ((4.11)/(4))^4 \\ t=4.53\text{ years} \end{gathered}`

therefore

the answer is

4.53 years