Question

A person invests $6675.00 at 6.25% compounded semiannually on October 1, 2018. If simple interest is allowed for part of an interest conversion period, how much is the investment worth June 1, 2022?

Answer 1

Sol:

Present value (PV) = $6675

As per the problem Simple interest is allowed for part of an interest conversion period. It means that any time moving away from the conversion time simple interest method will be use. Conversion period is semiannul (6 months) what it means that any months less than 6 months simple interest will be used, therefore 3 years and 6 months will be compounded semiannually, and the remaining two months will be calculated based on simple interest.

Interest rate (r) = 6.25%, Semiannual = 6.25/2 = 3.125%

Period (n) = From October 1, 2018 to June 1, 2022 - 3 years and 8 months, Semiannual = 3.5 x 2 = 7

Future value (FV) = PV x (1 + r)^n

Future value (FV) = 6675 x (1 + 3.125%)^7

Future value (FV) = 6675 x (1.03125)^7

Future value (FV) = $8279.402591

Therefore future value for 3.5 years will be $8279.402591

Now simple interest on remaining 2 months:

PV = $8279.402591

r = 6.25%

n = 2/12 = 0.1667

Interest amount = PV x r x n

Interest amount = 8279.402591 x 0.0625 x 0.1667

Interest amount = $86.24

Total FV = PV + Interest amount

Total FV = $8279.402591 + $86.24 = $8365.646368

Therefore investment will be approx worth $8365.65 on June 1, 2022