Find (a) the final amounts and (b) the total interest earned on the original investment.
1. $4500 is invested at 7.5% compounded annually for 6 years.
To find the final amount and total interest earned, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
Given:
P = $4500
r = 7.5% or 0.075 (converted to decimal)
n = 1 (compounded annually)
t = 6 years
(a) To find the final amount:
A = 4500(1 + 0.075/1)^(1*6)
Simplifying:
A = 4500(1.075)^6
Calculating the value inside the brackets:
A = 4500(1.513176155)
Final amount A = $6784.29
Therefore, the final amount after 6 years of compound interest is $6784.29.
(b) To find the total interest earned:
Total interest = Final amount - Principal amount
Total interest = $6784.29 - $4500
Total interest = $2284.29
Therefore, the total interest earned on the original investment is $2284.29.