Question

An amount of $7,000 is invested on 16 April 2020 at 10% pa compounded quarterly. Calculate the interest (I) earned between 16 April 2023 and 16 April 2027. Give your answer in dollars and cents to the nearest cent.

Answer 1

First of all lets calculate interest from 16/04/2020 to 16/04/2027 i.e 7 years

n = no of interest payments = 7 x 4 =28

r = rate of interest = 10%/4 = 2.5%

PV = 7000$

FV = PV(1+r)^n

=7000(1+2.5%)^28

=7000(1+0.025)^28

=7000(1.025)^28

=7000(1.9965)

=13975.47$

Thus interest = 13975.47 - 7000

= 6975.47$

Now lets calulate interest from 16/04/2020 to 16/04/2023 i.e 3 years

n = no of interest payments = 3 x 4 =12

r = rate of interest = 10%/4 = 2.5%

PV = 7000$

FV = PV(1+r)^n

=7000(1+2.5%)^12

=7000(1+0.025)^12

=7000(1.025)^12

=7000(1.34489)

=9414.22$

Thus interest = 9414.22 - 7000

= 2414.22$

Thus interest for period between 16 April 2023 and 16 April 2027. = Total interest - interest from 16/04/2020 to 16/04/2023

= 6975.47$ - 2414.22$

=4561.24 $