Between simple interest at 8% and compound interest at 9%, find the higher resulting balance after investing $500 for a period of 10 years. Round the answer to two decimal places.(1 point)
To compare the higher resulting balance between simple interest and compound interest, we need to calculate the balances for both scenarios after 10 years.
For simple interest, the formula to calculate the future value is:
FV = P(1 + rt)
Where:
FV = Future Value
P = Principal amount (initial investment)
r = Annual interest rate
t = Time period in years
For compound interest, the formula to calculate the future value is:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (initial investment)
r = Annual interest rate
n = Number of times interest is compounded per year
t = Time period in years
Given:
P = $500
r (Simple Interest) = 8% = 0.08
r (Compound Interest) = 9% = 0.09
t = 10 years
Calculating the future value for simple interest:
FV_simple = 500(1 + 0.08*10)
FV_simple = 500(1 + 0.8)
FV_simple = 500(1.8)
FV_simple = $900
Calculating the future value for compound interest compounded yearly:
FV_compound_yearly = 500(1 + 0.09)^10
FV_compound_yearly = 500(1.09)^10
FV_compound_yearly = 500(1.9477)
FV_compound_yearly = $973.85
Comparing the resulting balances, we can see that the higher resulting balance after investing $500 for 10 years is $973.85 with compound interest at 9%.