Answer:
0.4868%
$615.47
Explanation:
Given that
a. EAR = 6%
Thus,
Equivalent monthly rate = (1 + r)^n - 1
Where r = EAR
Therefore
= (1 + 0.06)^1/12 - 1
= 1.0048675 - 1
= 0.0048675 × 100
= 0.4868%
b. Given that
Monthly rate = 0.4868%
Future value = 100,000
Time = 10 years
Recall that
FV annuity formula = C × (1/r) × ([1 + r ]^n - 1)
Where
C = payment
Therefore
100000 = C (1/0.004868) × ([1 + 0.004868]^120 - 1)
C = 100,000/(1/0.004868) × ([1 + 0.004868]^120 - 1)
C = $615.47 per month
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:
[tex]Fv = C[((1+i)^n -1)/i][/tex]
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.
