For her daughter's university education, Carla Hackl has invested an inheritance in a fund paying 9.2%...

For her daughter's university education, Carla Hackl has invested an inheritance in a fund paying 9.2% compounded quarterly. If ordinary annuity payments of $4750.00 per month are to be made out of the fund for 5 years and the annuity begins 9.75 years from now, how much was the inheritance?

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Expert Solution

Solution

Ordinary Annuity

When the quarterly deposits are made at end of the every quarter then it is knowing as ordinary annuity

We can use the formula for finding the future value as below

A = p x [ ( 1 + (r/n) )^nt-1 ] / ( r/n )

Here A = future value = $?

p = Cash flow per period = $4750

r = rate of interest = 9.2% = 9.2/100 = 0.092

n = compounding frequency is quarterly so n= 4

t = Number of years = 9.75 years = 9.75 x 4 = 39 quarters

A = 4750 x [ ( 1 + (0.092/4 ))^4(9.75) – 1 ] / (0.092/1)]

A = 4750 x [ ( 1 + (0.023 ))⁽³⁹⁾ – 1 ] / (0.023)]

A = 4750 x [ ( 1.023 ))⁽³⁹⁾ – 1 ] / (0.023)]

A = 4750 x [ 2.427446767 – 1 ] / (0.023)]

A = 4750 x [ 1.427446767 ] / (0.023)]

A = 4750 x [ 62.0629]

A = 294798.79

jeff jeffy answered 1 year ago

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