Question

5
Keisha borrowed $8000 at a rate of 9.5%, compounded semiannually. Assuming she makes no payments, how much will she owe after 9 years?
Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

Answer:

Keisha will owe $18444.32 after 9 years

Step-by-step explanation:

Compound Interest

It occurs when the interest is added to the principal rather than paying it in.

It basically means paying interest over 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

Keisha borrowed P = $8000 at a rate of r = 9.5% = 0.095 (assumed annual rate) compounded semiannually (twice a year).

If she makes no payments, the amount she owes increases over time. After t = 9 years, we can calculate the amount owed by using the above formula.

Please, note that since there are 2 compounding periods per year, n = 2, thus:

$\displaystyle A=8000\left(1+{\frac {0.095}{2}}\right)^{2\cdot 9}$

Operating:

$\displaystyle A=8000\left(1+0.0475\right)^{18}$

$A = 8000\cdot 2.30554$

A = $18444.32

Keisha will owe $18444.32 after 9 years