Question

In: Finance

You would like to have $650,000 when you retire in 40 years. How much should you...

You would like to have $650,000 when you retire in 40 years. How much should you invest each quarter if you can earn a rate of 2.7% compounded quarterly?

a) How much should you deposit each quarter?

b) How much total money will you put into the account?

c) How much total interest will you earn?

Expert Solution

(a) Here, the deposits will be same every quarter, so it is an annuity. The future value of annuity is $650000. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity = $650000, P is the periodical amount, r is the rate of interest = 2.7% compounded quarterly. So quarterly rate = 2.7% / 4 = 0.675% and n is the time period = 40 * 4 = 160 quarters.

Now, putting these values in the above formula, we get,

$650000 = P * ((1 + 0.675%)¹⁶⁰- 1 / 0.675%)

$650000 = P * ((1 + 0.00675)¹⁶⁰ - 1 / 0.00675)

$650000 = P * ((1.00675)¹⁶⁰- 1 / 0.00675)

$650000 = P * (2.93401361434 - 1/ 0.00675)

$650000 = P * (1.93401361434 / 0.00675)

$650000 = P * 286.520535458

P = $650000 / 286.520535458

P = $2268.60

So, the amount of money that we need to deposit each quarter is $2268.60.

(b) Total money that will be put into account = $2268.60 * 160 = $362976

(c) Total interest = Future value - Total money invested

Total interest = $650000 - $362976 = $287024

jeff jeffy answered 7 months ago

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