When investing money that is compounded annually, which option will earn the most interest?
A interest rate of 8.00% per annum, invested for 7 years
b. interest rate of 6.00% per annum, invested for 9 years
c. interest rate of 7.00% per annum, invested for 8 years
d. interest rate of 9.00% per annum, invested for 6 years
To determine which option will earn the most interest, we need to calculate the compounded amount for each option and compare the final amounts.
Option A:
Principal amount = $1
Interest rate = 8.00% per annum
Number of years = 7
Compound amount = Principal amount * (1 + interest rate/100)^number of years
= $1 * (1 + 8.00%/100)^7
= $1 * (1 + 0.08)^7
= $1 * (1.08)^7
≈ $1.7182
Option B:
Principal amount = $1
Interest rate = 6.00% per annum
Number of years = 9
Compound amount = Principal amount * (1 + interest rate/100)^number of years
= $1 * (1 + 6.00%/100)^9
= $1 * (1 + 0.06)^9
= $1 * (1.06)^9
≈ $1.7125
Option C:
Principal amount = $1
Interest rate = 7.00% per annum
Number of years = 8
Compound amount = Principal amount * (1 + interest rate/100)^number of years
= $1 * (1 + 7.00%/100)^8
= $1 * (1 + 0.07)^8
= $1 * (1.07)^8
≈ $1.7187
Option D:
Principal amount = $1
Interest rate = 9.00% per annum
Number of years = 6
Compound amount = Principal amount * (1 + interest rate/100)^number of years
= $1 * (1 + 9.00%/100)^6
= $1 * (1 + 0.09)^6
= $1 * (1.09)^6
≈ $1.6334
Comparing the compound amounts, it can be observed that Option C with an interest rate of 7.00% per annum invested for 8 years will earn the most interest. The compound amount in Option C is approximately $1.7187, which is the highest among all the options provided.