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Quarterly deposits are made into a fund at the beginning of each quarter starting today for...

Quarterly deposits are made into a fund at the beginning of each quarter starting today for 5 years. The first 8 deposits are $1000 each and deposits increase by 1% per quarter thereafter. If the fund earns 8% effective annually, find the accumulated value at the end of 5 years.

Please explain which equations you used and do not use excel.

Expert Solution

Quartertly deposits for 2 years = $1,000

Growth rate of Quarterly deposits after 2 years = 1%

Effective Interest rate = 8%

where r is the nominal quarterly rate

m is the number of compounding periods

i is the effective interest rate

r = 0.07771/4 = 0.01943 or 1.943%

The equation to find out future value of deposits is given below

Where F is the future value

P is the deposit

r is the quarterly interest rate

m is the total number of compounding periods (Quarters)

Number of quarters in first two years = 2*4 = 8

Value of deposits for the first two years =

Value of deposits for the first two years = $8565.70

The equation for the future value of a growing annuity is given below

where g is the growth rate

Number of quarters after two years = 3*4 = 12

growth rate = 1% = 0.01

Future Value after two years is equal to:

Future Value after two years = $14,097.37

Total Value after 5 years = $8,565.70 + $14,097.37 = $22,663.07

jeff jeffy answered 2 years ago

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