Suppose your bank account pays interest monthly with an effective annual rate of 6%. What amount of interest will you earn each month? If you have no money in the bank today, how much will you need to save at the end of each month to accumulate $100,000 in 10 years?

The monthly interest rate is 0.5%

The monthly savings must be $610.21

Explanation:

Firstly we are given an effective annual rate of 6% therefore to find the effective monthly rate we will divide this interest rate by 12 months as a year has 12 months, the monthly rate is 6%/12= 0.5%.

To now calculate the the monthly savings we will use the future value annuity as this is the monthly deposits that will accumulate an interest in 10 years to be a future amount of $100000, so to simplify the given information :

$100000 is the future value of the monthly savings Fv

0.5% is the monthly interest rate i

10 years  x 12 months = 120 payments is the number of saving deposits in 10 years.

now we will substitute the above information to the following future value formula:

C is the monthly savings deposits that will be accumulated during the 10 year course in which we will calculate.

$100000 = C[(1+0.5%)^120 -1)/0.5%] after substituting we solve for C

$100000/[(1+0.5%)^120 -1)/0.5%] = C

$610.2050194 = C now we round off to two decimal places.

$610.21 = C is the monthly savings that will accumulate to $100000 in 10 years.

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