Asked by Michael Lasorsa on Apr 26, 2024
Verified
What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months?
A) $8690.00
B) $6331.04
C) $4684.05
D) $999.14
E) $3488.73
Compounded Semiannually
Interest calculated twice per year, with the first period's interest being added to the principal before the second period's interest is calculated.
- Ascertain the period needed for the growth, depreciation, or maturation of investments under distinct interest rates.
- Calculate the interest accrued on different loans and investments.
Verified Answer
AO
Ayomide OlowookereApr 28, 2024
Final Answer :
C
Explanation :
To find the initial amount invested (the principal, P), we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. Given A = $6380, r = 10% or 0.10, n = 2 (since it's compounded semiannually), and t = 38 months or 38/12 years, we solve for P. Rearranging the formula to solve for P gives P = A / (1 + r/n)^(nt). Substituting the given values and solving for P gives the correct answer.
Learning Objectives
- Ascertain the period needed for the growth, depreciation, or maturation of investments under distinct interest rates.
- Calculate the interest accrued on different loans and investments.