Question

a debt of $10,000 due ten years from now is instead to be paid off by three payments: $1000 now, $2000 in three years, and a final payment at the end of six years. what would this payment be if an interest rate of 8% compounded semiannually is assumed? ​

Answer 1

Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. Thought to have originated in 17th-century Italy, compound interest can be thought of as "interest on interest," and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount.

Compound interest = total amount of principal and interest in future (or future value) less principal amount at present (or present value)

= [P (1 + i)n] – P

= P [(1 + i)n – 1]

Where:

P = principal

i = nominal annual interest rate in percentage terms

n = number of compounding periods

Take a three-year loan of $10,000 at an interest rate of 5% that compounds annually. What would be the amount of interest? In this case, it would be:

$10,000 [(1 + 0.05)3 – 1] = $10,000 [1.157625 – 1] = $1,576.25

Step-by-step explanation:

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