Question

Ten years from today you must make a payment of $1,432.02. To prepare for this payment, you will make 5 equal deposits, beginning today and for the next 4 quarters, in a bank that pays a nominal interest rate of 12 percent, quarterly compounding. How large must each of the 5 payments be?

Answer 1

Answer:

The payment will be for 90.35

Explanation:

It will made 5 payment during the course of a year and then, 9 years from that date will need to pay 1,432.02

timeline:

<---/---/---/---/---/-----------------------------------------------//-->

  payments                                                         obligation

we will move the payment at the time of the last patment, as they will generate a future value.

We will bring the 1,432.02 to the same date.

The future value generate from the payment must equalt the present valeu fothe obligation

the payment will be the present value of a lump sum

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,432.02

time   36.00  (9 years x 4 quarter per year)

rate  0.03 (12 % over 4 quarter a year)

$\frac{1432.02}{(1 + 0.03)^{36} } = PV$  

PV   494.09

Then, we calcualte future value of the payment

the payment will be an annuity due for 5 periods

$FV \div \frac{(1+r)^{time} -1}{rate}(1+0.03) = C$

FV  $494.09

time 5

rate 0.03

$494.09 \times \frac{(1+0.03)^{5} -1}{0.03}(1+0.03) = C$

C  $ 90.354