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 when compounded annually, we need to calculate the final amount for each option.
a. interest rate of 6.00% per annum, invested for 1 year:
Final amount = initial amount * (1 + interest rate)^time
Final amount = initial amount * (1 + 6/100)^1
Final amount = initial amount * 1.06
b. interest rate of 5.00% per annum, invested for 2 years:
Final amount = initial amount * (1 + interest rate)^time
Final amount = initial amount * (1 + 5/100)^2
Final amount = initial amount * 1.1025
c. interest rate of 3.00% per annum, invested for 4 years:
Final amount = initial amount * (1 + interest rate)^time
Final amount = initial amount * (1 + 3/100)^4
Final amount = initial amount * 1.1255
d. interest rate of 4.00% per annum, invested for 3 years:
Final amount = initial amount * (1 + interest rate)^time
Final amount = initial amount * (1 + 4/100)^3
Final amount = initial amount * 1.1256
Comparing the final amounts:
a. final amount = initial amount * 1.06
b. final amount = initial amount * 1.1025
c. final amount = initial amount * 1.1255
d. final amount = initial amount * 1.1256
Based on these calculations, Option D with an interest rate of 4.00% per annum, invested for 3 years, will earn the most interest per year.