Question

Douglas bought a store and agreed to pay 100000 at the end of every six months for seven years. What is the equivalent cash price of the store if the interest rate is 5% compounded quarterly?

Answer 1

Douglas bought a store and agreed to pay 100000 at the end of every six months for seven years

so each year he pays twice 100000 twice.

Amount he can pay for 7 years $=2\times 100000 \times 7=1400000$

If he opt to follow the second payment method, equivalent cash price of the store if the interest rate is 5% compounded quarterly can be calculated as follows.

$A=P(1+r)^n$

Since he is paying 100000 after every 6 months, so in a year he pays P=100000+100000=200000

$, n=4\times 7=28, r=5/4=1.25\%$

$A=200000(1+1.25/100)^{28}=283198.4607$