When investing money that is compounded annually, which of the following options will earn the most of interest per year?

Question

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

Answer 1

To determine which option will earn the most interest per year, we can calculate the compound interest for each option using the formula:

A = P(1 + r/n)^(nt)

where:
A = the final amount after compound interest
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

Calculating the compound interest for each option:

a. interest rate of 6.00% per annum, invested for 1 year:
A = P(1 + r/n)^(nt)
A = P(1 + 0.06/1)^(1*1)
A = P(1 + 0.06)^1
A = P(1.06)

b. interest rate of 5.00% per annum, invested for 2 years:
A = P(1 + r/n)^(nt)
A = P(1 + 0.05/1)^(1*2)
A = P(1 + 0.05)^2
A = P(1.05)^2

C interest rate of 3.00% per annum, invested for 4 years:
A = P(1 + r/n)^(nt)
A = P(1 + 0.03/1)^(1*4)
A = P(1 + 0.03)^4
A = P(1.03)^4

D interest rate of 4.00% per annum, invested for 3 years:
A = P(1 + r/n)^(nt)
A = P(1 + 0.04/1)^(1*3)
A = P(1 + 0.04)^3
A = P(1.04)^3

Comparing the options, the highest value of A (the final amount after compound interest) will yield the most interest per year. So, we need to find the option with the highest value when the principal amount P is multiplied by the corresponding interest rate:

a. A = P(1.06)
b. A = P(1.05)^2
C. A = P(1.03)^4
D. A = P(1.04)^3

Given that the interest rates are equal for each option, we can ignore P and focus on the values after multiplying the interest rates:

a. 1.06
b. 1.05^2 = 1.1025
C. 1.03^4 = 1.1255 approximately
D. 1.04^3 = 1.124864 approximately

Comparing these values, option C has the highest value of approximately 1.1255. Therefore, the interest rate of 3.00% per annum, invested for 4 years, will earn the most interest per year.