Question

Problem 3-19 (algorithmic) Question What is the amount of the quarterly deposits A such that you will be able to withdraw the amounts shown in the cash flow diagram if the interest rate is 8% compounded quarterly? $2,400 8% Compounded quarterly $1,700 1 Quarters 1 2 3 4 5 6 7 0 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 А (Deposit) The amount of the quarterly deposits A should be $ (Round to the nearest dollar.)

Answer 1

Answer is $435

Explanation:

In the given problem there are two withdrawal, first one at the end of quarter 4 of $ 1,700 and second one at the end of quarter 8 of $2,400

A required to deposit amount quarterly starting with quarter 0, hence total number of deposit by A is 9

For calculation quarterly deposit first we should calculate the quarterly interest applicable as interest rate is given as 8% compounded quarterly

Next we calculate present value of both withdrawals

Next we equate the present value of both deposit with present value factor of all quarterly deposit and find the quartely deposit.

Step 1:- Calculation of Interest Rate = Annual Interest Rate / Number of period = 8% / 4 = 2%

Step 2:- Present value of both withdrawals

= Present Value of $1,700 at quarter 4 + Present Value of $2,400 at quarter 8

= [$1,700 * PVF(2%,4)] + [$2,400 * PVF(2%,8)]

= ($1,700 * 0.9238) + ($2,400 * 0.8535)

= $1,570.46 + $2,048.40

= $3,618.86

Step 3:- Present Value factor of all quaterly deposit

= PVAF(2%,8) + 1

= 7.3255 + 1

= 8.3255

Step 4 Equating Present Value of all deposit with present value of both withdrawals

Present Value of all deposits = 8.3255 * Quaterly Deposit

Present value of all withdrawals = $3,618.86

By equating both present values we get

= 8.3255 * Quarterly Deposit = $3,618.86

Quarterly Deposit = $3,618.86 / 8.3255 = $ 434.67 = $435 (rounding to nearest dollar)