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Brut [27]
2 years ago
5

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

onth? 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?
Business
2 answers:
Anna [14]2 years ago
5 0

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:

Fv = C[((1+i)^n -1)/i]

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.

Bess [88]2 years ago
4 0

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

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