Help please and thank you

Question

Michael borrowed $8000 at a rate of 7%, compounded semiannually. Assuming he makes no payments, how much will he owe after 7 years?

Do not round any intermediate computations, and round your answer to the nearest cent.

$______

Answer 1

Because the interest is compounded annually (and not continuously), then use the formula: y = y₀(1 + r/n)^nt

1. y is the current amount at any time: this is the question
2. y₀ is the initial amount (or the principal amount): $8000
3. r is the rate expressed as a decimal: 7% = 0.07
4. n is the amount of time the interest is compound PER YEAR: semiannually = 2
5. t is time in YEARS: 7 years

It is important that there are no payments made towards the loan. Then we can substitute into the formula once:

y = y₀(1 + r/n)^nt = 8000(1 + 0.07/2)²⁽⁷⁾ = 8000(1.035)¹⁴ = $12,949.556 = $12,949.56