Question

Joan is saving up money for a down payment on a motorcycle. She currently has $2744, but knows she can get a loan at a lower interest rate if she can put down $3688. If she invests the $2744 in an account that earns 5% annually, compounded monthly, how long will it take Joan to accumulate the $3688? Round your answer to two decimal places, if necessary.

Answer 1

Approximately 71 .11 months

Step-by-step explanation:

This is a Future Value question. However we are solving for the Number of periods to determine how long it would take Joan to accumulate $3688.

Interest compounded monthly means Joan will be paid interest on her deposit on an annual basis prorated. she gets to earn interest on the accumulation of interest + principal monthly.

The formular for calculating Future Value is

FV = PV ( 1 + R )ⁿ

Our R which is the Rate(5%) will be adjusted to 12 months. =

`(0.05)/(12)`

However we need to solve for the N since we already have our FV. Therefore the revised formular is :

`(log((FV)/(PV)))/(log(1+R))`

Continuing with the formular

`(log((3688)/(2744)))/(log(1+0.00417))`

Which is equals to 71.11 months approximately 6 years.