Question

ABC Company deposits $25,000.00 with First National Bank in an account earning
6% annual interest, compounded semi-annually.
How much will ABC have in the account after 5 years?

Answer 1

The formula that we have to use to calculate the amount that we will have in bank after 5 years is as follow.

A = P (1 + r/n) ^(nt)

Principle (Lets Denote it with "P") deposited $ 25,000.00, so P= $ 25,000.00. This is basically amount deposited.

6% is the annual interest rate . Lets denote the rate of interest as "r" . r=6/100 that is 0.06 {we have removed the sign of the percentage so that we can readily use the formula}.

"n " denotes the no of times interest will be compounded in a year. In the instant case interest is compounded semiannually so we can say , interest is compounded two times in a year. So n=2

"t" denotes the number of year for which the money is invested. In our case its 5 years, So t=5.

nt=10 (that is n*t). nt means , in total how many times we compounded our interest in a span of 5 years.

In the instant case we have to compute the amount (Lets Denote it with "A") that we will be receiving after 5 years.

Now putting all the things in formula we get the Amount as follow.

A= $25,000(1+0.06/2)^(2*5)

A=$25,000*(1.03)¹⁰

A=$25,000*1.343916

A= $33,597.91 this is what ABC will have it in the account after 5 years.