Question

You borrowed $1,690 for 5 1/2 years at 5.7% compounded semianually. what total will you pay back?​

Answer 1

You will pay $2,302 back.

Explanation:

Compound interest occurs when the interest is reinvested rather than paying it out. When it happens 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}{n}}\right)^(nt)}`

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

We are given the following conditions: Principal amount P=$1,690, duration=5 1/2 years, interest rate r=5.7% compounded semi-annually.

Note we don't actually have the value of n or t because they must be taken from the duration and the compounding period.

The interest compounds semi-annually i.e. twice a year. Thus, n=2.

The interest rate is converted to decimal r=0.057 and we apply the formula:

`{\displaystyle A=1,690\left(1+{\frac {0.057}{2}}\right)^(2*5.5)}`

`{\displaystyle A=1,690\left(1+0.0285\right)^(11)}`

A=$2,302

You will pay $2,302 back.