Question

Find the balance on the account after 6.2 years if $150000 was invested at an annual interest rate of 2.76% and the interest was compounded continuously. What is the accumulated value if the money is compounded continuously? Round to the nearest cent.

Answer 1

Annual compounding gives $177,582.70

Continuous compounding gives $ 177,994.97

Explanation:

In the first place, the balance on account can be computed using the future value formula given below:

FV=PV*(1+r)^N

FV is the future value which is unknown

PV is the amount invested at time zero which is $150,000

r is the rate of return on the investment at 2.76%

N is the period of investment which is 6.2 years

FV=$150,000*(1+2.76%)^6.2

FV=$ 177,582.70

However if the continuous compounding is opted for the accumulated value is computed thus:

FV=PV* e^(rs*N)

where e is constant figure given as 2.7182818

rs is the rate of return at 2.76%

N is 6.2 years

PV is $150,000

FV=$150,000*2.7182818^(2.76%*6.2)

FV=$150,000*1.186633134

FV=$ 177,994.97