F.5 MATHS

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Question :

Felix family has decided to deposit $350 into an annuity
every 3 months for 4 years. The account will earn 3.75% a
compounded quarterly. Starting 3 months after the last
deposit, Felix will withdraw the money every 3 months
inequal payments for 2 years. What is the amount of each
withdrawal?

Solution :

Figure out the balance in the account after the deposits are
made. The family will make a total of 16 payments over 16
quarterly periods. Since the interest rate given is annual,
divide it by 4 to get the quarterly interst rate: 0.375 ÷ 4 =
0.09375. Then find the future value of an annuity of $350 at
9.375% for 16 periods.

Method 1 : use financial calculator
Set PV = 0 (the present value is zero, since no payments
have been made), PMT = - 350 (the payment made each
period; it is negative since this is a cash outflow), N or PER
or NPER (the number of periods, depending on your
calculator) = 16, and INT = 0.09375; use the calculator to
find FV (future value).

Method 2 : use Excel
The formula is =FV(0.009375,16,-350). Excel assumes PV = 0.

Method 3 : use an annuity table
Use an annuity table to find the future value of an annuity
of $1 at 9.375% for 16 periods. The value should be close to
17.1758; multiply this by 350 to get the value of an annuity
of $350.

Whichever method you use, the answer should be $6012.

Now figure out how much Felix can withdraw each quarter.

Method 1 : use financial calculator
- 6012 is the present value. 0 is the future value. There are 8
periods and the interest rate is 0.09375. Calculate the payment.

Method 2 : use Excel
The formula is =PMT(0.009375,8,-6012).

Method 3 : use an annuity table
Look for the present value of the annuity this time rather
than the future value. You need the present value of an
annuity of $1 at 9.375% for 8 periods. The value should be
close to $7.67. The present value of an annuity of x dollars
is 7.67x = 6012. Then find the value of x.

Finally, the answer should be $784.

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