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.

Approximately 71 .11 months

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. =

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

Continuing with the formular

Which is equals to 71.11 months approximately 6 years.

gather the things you’ll need. it’s best to have a parent or guardian to you open an account. the parent or guardian can co-sign your account, which means that they’ll sponsor you. as co-signers, they’ll need to bring two forms of current photo id. if they only have one piece of photo id, their second id may be a current major credit card or gas card.