When investing money that is compounded annually, which of the following options will earn the most of interest per year?
a. interest rate of 6.00% per annum, invested for 1 year b. interest rate of 5.00% per annum, invested for 2 years
c. interest rate of 3.00% per annum, invested for 4 years
d. interest rate of 4.00% per annum, invested for 3 years
To determine which option will earn the most interest per year, we need to calculate the compound interest for each option.
a. For option a, the interest rate is 6.00% per annum, and the investment is for 1 year. The compound interest is:
= Principal amount * (1 + interest rate)^time - Principal amount
= 1 * (1 + 0.06)^1 - 1
= 1 * 1.06 - 1
= 0.06
b. For option b, the interest rate is 5.00% per annum, and the investment is for 2 years. The compound interest is:
= Principal amount * (1 + interest rate)^time - Principal amount
= 1 * (1 + 0.05)^2 - 1
= 1 * 1.1025 - 1
= 0.1025
c. For option c, the interest rate is 3.00% per annum, and the investment is for 4 years. The compound interest is:
= Principal amount * (1 + interest rate)^time - Principal amount
= 1 * (1 + 0.03)^4 - 1
= 1 * 1.1255 - 1
= 0.1255
d. For option d, the interest rate is 4.00% per annum, and the investment is for 3 years. The compound interest is:
= Principal amount * (1 + interest rate)^time - Principal amount
= 1 * (1 + 0.04)^3 - 1
= 1 * 1.124864 - 1
= 0.124864
Comparing the compound interests, we find that option c (interest rate of 3.00% per annum, invested for 4 years) will earn the most interest per year with a compound interest of 0.1255.