Question

Dale takes out a loan of $8,000 with a 15.2% interest rate that is compounded semi-annually.

If he pays off the loan in 3 years, how much will he end up paying?
Round your answer to the nearest cent.
DO NOT round until you have calculated the final answer.

Answer 1

Answer: 12,415.48

Step-by-step explanation:

Use the compund interest formula for calculating the future value, A=P(1+rn)n⋅t where A is the unknown future value, P is the principal, so P=$8,000, r is the rate written as a decimal, so r=0.152, n is the number of periods of compounding which is 2 when compounded semi-annually,so n=2, and t is the time in years, so t=3. Substitute the values into the formula.

Use the compound interest formula and substitute the given values: A=$8,000(1+0.1522)2(3). Simplify using the order of operations: A=$8,000(1.076)6=$8,000(1.551935358)≈$12,415.48.

Answer 2

$12,415.48

Step-by-step explanation:

The formula for calculating compound interest is

FV = PV × (1+r)^ n.

For Dale , FV = the amount he will pay?

PV = $8,000

r = 15.2%

n =3 years

Since interest is compounded semi-annually, the applicable r will be 15.2% divided by 2, n will be 3 years x 2

Fv= $8,000 x ( 1 + {15.2 %/ 2}^6

Fv = $8,000 x (1+ 7.6/100) ^ 6

Fv= $8,000 x ( 1.076) ^6

Fv = $8000 x 1.551934858492184

Fv=$12,415.482

Fv= $12,415.48

Dale will end up paying $12,415.48