Question

find the amount accumlatrd after investing a principal P for t years at an interest rate compound annuay. P= $12,000 r=7.5% t=7 ​

Answer 1

A = $19,908.59

Explanation:

Compound Interest

Compound interest occurs when the interest earned in a given period is reinvested rather than paying it out. The interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

`{\displaystyle A=P\left(1+{\frac {r}{k}}\right)^(kt)}`

Where:

A = final amount

P = initial principal balance

r = interest rate

k = number of times interest applied per time period

t = number of time periods elapsed

We are given the following data:

P = $12,000

r = 7.5% = 7.5/100 = 0.075

t = 7

k = 1 since there is only on compounding per year.

Applying the formula:

`{\displaystyle A=\$12,000\left(1+{\frac {0.075}{1}}\right)^(7)}`

`{\displaystyle A=\$12,000\left(1.075\right)^(7)}`

A = $19,908.59