Question

How much would your parents have to deposit each month into an account that grows at a rate of 7% per year compounded quarterly if they want to have $88,000 at the end of year 4 to cover part of your college expenses? Assume no interperiod compounding.

Parents have to deposit $ _________ each month.

Answer 1

Answer:

Given that :

how much would your parents have to deposit each month into an account that grows at a rate

of 7% per year compounded quarterly if they want to have $88,000 at the end of year 4 to cover

part of your college expenses.

Let the monthly deposit be x

Since there is no inter period compounding, deposits are assumed to have taken place at the end of quarter i.e.

Quarterly deposit=3*x

Quarterly rate of interest=i=7%/4=1.75%

Number of deposits=n=4*4=16

F W of deposits=$88000

We know that

F W=3 x*(F/A,0.0175,16) or

88000=3 x*(F/A,0.0175,16)

Let us calculate the interest factor

(1 + i) - 1 (F/A, i,n)=

(F/A, 0.0175,16) = (1 +0.0175) 16 - 1 = 18.281677 0.0175

Plug in value of interest factor in above equation

88000=3 x*18.281677

x=88000/(3*18.281677)=$1604.52 per month