Suppose your bank account pays interest monthly with an effective annual rate of 6%. What amount of interest will you earn each m
2 answers:
Answer:
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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