Question

Sandra Robinson is saving to buy a house in five years. She plans to put 20 percent down at that time, and she believes that she will need $26,000 for the down payment. If Sandra can invest in a fund that pays 7.20 percent annual interest, compounded quarterly, how much will she have to invest today to have enough money for the down payment? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to the nearest penny.)

Answer 1

Answer:

Sandra will deposit $  18,197.75

Explanation:

It need to obtain 26,000 dollars in five years.

She will invest at 7.20 annual compounding quarterly.

We need to know to calculate the lump sum Sandra needs to deposit today.

We use present value of a lump sum formula:

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

Maturity  $26,000

time   20 (five years x 4 quarters per year)

rate  0.018 (7.2 / 4 quarter per year)

$\frac{26000}{(1 + 0.018)^{20} } = PV$  

PV   18,197.75