Question

 

A principal of

​$5500

is invested in an account paying an annual rate of

4​%.

Find the amount in the account after

6

years if the account is compounded​ semiannually, quarterly, and monthly.

​(a) The amount in the account after

6 years if the account is compounded semiannually is $

Answer 1

Answer: (a) $6975.33, (b) $6983.54 and (c) $6989.06

Explanation: Principal amount, P=$5500, annual interest rate, r=4%=4/100=0.04, time, t=6 years. Let the accumulative amount after 6 year will be, A=?

The equation governing the accumulative amount, principal amount, interest rate, and time is given by

------------------------------------------- (1)

where, A=accumulative amount, P=Principal amount, r=annual interest rate, t=time (in years) and n denotes the frequency by which an interest in counted in a year.

For, semiannualy, n=2, for quarterly, n=4, for montly, n=12.

(a) For compound interest counted semiannually, n=2. So, from eqn 1

(b) For compound interest counted quarterly, n=4

(c) Compound interest counted montly, n=12