a. Use the appropriate formula to determine the periodic deposit.

b. How much of the financial goal comes from deposits and how much comes from interest?

Solutions

Expert Solution

(a) Here, the deposits will be same every month, so it is an annuity. The future value of annuity is $180000. 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 = $180000, P is the periodical amount, r is the rate of interest = 4.5% compounded monthly. So monthly rate = 4.5% / 12 = 0.375% and n is the time period = 12 * 12 = 144 months

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

$180000 = P * ((1 + 0.375%)¹⁴⁴- 1 / 0.375%)

$180000 = P * ((1 + 0.00375)¹⁴⁴- 1 / 0.00375)

$180000 = P * ((1.00375)¹⁴⁴- 1 / 0.00375)

$180000 = P * ((1.71427461161- 1) / 0.00375)

$180000 = P * (0.71427461161 / 0.00375)

$180000 = P * 190.473229763

P = $180000 / 190.473229763

P = $945.01

So, the periodic deposit is $945.01

(b) Financial goal from deposits = $945.01 * 144 = $136081.44

Financial goal from interest = $180000 - $136081.44 = $43918.56

jeff jeffy answered 1 year ago

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