SOLUTION: Suppose that Jake plans to deposit money into an account earning 5.9% compounded monthly. a.) If he decides to deposit $4000 into the account, how much interest would he earn in

Algebra ->  Finance -> SOLUTION: Suppose that Jake plans to deposit money into an account earning 5.9% compounded monthly. a.) If he decides to deposit $4000 into the account, how much interest would he earn in      Log On


   

Question 629263: Suppose that Jake plans to deposit money into an account earning 5.9% compounded monthly.
a.) If he decides to deposit $4000 into the account, how much interest would he earn in four years?
b.) How much would his deposit have to be if he wanted to have a total of at least $10,000 after four years?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The formulas to use are FUTURE VALUE OF A PRESENT AMOUNT AND PRESENT VALUE OF A FUTURE AMOUNT.

The reference for these formulas can be found here:
http://www.algebra.com/algebra/homework/Finance/FINANCIAL-FORMULAS-101.lesson

The formulas are shown below:

FUTURE VALUE OF A PRESENT AMOUNT
FV%28PA%29+=+PA+%2A+%281%2Bi%29%5En
FV = Future Value
PA = present amount
i = Interest Rate per Time Period
n = Number of Time Periods

You would use the following values in the future value formula:

FV = what you want to find.
PA = 4000
i = 5.9% / 100 = .059 / 12 = .0049167 per month (rounded to 7 decimal places)
n = 4 * 12 = 48 months.

Your answer should be 5061.78 rounded to 2 decimal places.

The interest earned is 5061.78 - 4000 = 1061.78


PRESENT VALUE OF A FUTURE AMOUNT
PV%28FA%29+=+FA+%2F+%28%281%2Bi%29%5En%29+
PV = Present Value
FA = future amount
i = Interest Rate per Time Period
n = Number of Time Periods

You would use the following values in the future value formula:

PV is what you want to find.
FA = 10000
i = .0049167 per month (rounded to 7 decimal places)
n = 48

Your answer should be 7902.36 rounded to 2 decimal places.

That's how much he would have to deposit to end up with $10,000 in 4 years.
Confirm by sticking 7902.36 rather than 4000 in the future value of a present amount formula and you will find that the future value is 10,000.

It's actually 9,999.996762, but the difference is due to rounding error. Carry the decimals further out and you'll get a lot closer and eventually right on if you carry enough decimal places.