Serenity wants to invest $25,000 of her savings for her retirement fund. Determine the difference in interest earnings between a 10% simple interest rate and a 7% compound interest rate with interest being compounded annually if Serenity invests her money for 25 years. Round the answer to two decimal places as needed
Serenity wants to invest $25,000 of her savings for her retirement fund. Determine the difference in interest earnings between a 10% simple interest rate and a 7% compound interest rate with interest being compounded annually if Serenity invests her money for 25 years. Round the answer to two decimal places as needed.
To calculate the simple interest, we use the formula: Interest = Principal * Rate * Time
For the simple interest, the principal is $25,000, the rate is 10%, and the time is 25 years.
Interest (simple) = $25,000 * 0.10 * 25 = $62,500
To calculate the compound interest, we use the formula: A = P(1 + r/n)^(nt) - P
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
For the compound interest, the principal is $25,000, the rate is 7%, the time is 25 years, and interest is compounded annually.
Interest (compound) = $25,000 * (1 + 0.07/1)^(1*25) - $25,000
= $25,000 * (1.07)^(25) - $25,000
= $25,000 * 1.967151 - $25,000
= $49,178.77
Difference in Interest Earnings = Interest (compound) - Interest (simple)
= $49,178.77 - $62,500
= -$13,321.23
The difference in interest earnings between the 10% simple interest rate and the 7% compound interest rate, compounded annually, after 25 years would be -$13,321.23.
To calculate the simple interest, we use the formula: Interest = Principal * Rate * Time
For the simple interest, the principal is $25,000, the rate is 10%, and the time is 25 years.
Interest (simple) = $25,000 * 0.10 * 25 = $62,500
To calculate the compound interest, we use the formula: A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
For the compound interest, the principal is $25,000, the rate is 7%, the time is 25 years, and interest is compounded annually.
Interest (compound) = $25,000 * (1 + 0.07/1)^(1*25) - $25,000
= $25,000 * (1.07)^(25) - $25,000
= $25,000 * 3.869685 - $25,000
= $96,742.13 - $25,000
= $71,742.13
Difference in Interest Earnings = Interest (compound) - Interest (simple)
= $71,742.13 - $62,500
= $9,242.13
The difference in interest earnings between the 10% simple interest rate and the 7% compound interest rate, compounded annually, after 25 years would be $9,242.13.