Question
Dawson and Adam have $3,00. Dawson thinks they will earn more interest if they put it in the bank for 2 1/2 years at an interest rate of 5.5%. Adam thinks they will earn more interest if they put it in the bank for four years at an interest rate of 4.5%. who is correct? explain
Answers
GPT 3.5
To determine who is correct, we need to calculate the total amount of money that Dawson and Adam will have after the specified time periods.
Dawson:
Principal amount = $3,000
Time = 2.5 years
Interest rate = 5.5%
The formula to calculate the compound interest is A = P(1 + r/n)^(nt), where:
A = the future value of the investment
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Applying the formula, we have:
A = 3000(1 + 0.055/1)^(1*2.5)
A = 3000(1.055)^(2.5)
A ≈ $3,428.52
Adam:
Principal amount = $3,000
Time = 4 years
Interest rate = 4.5%
Applying the same formula:
A = 3000(1 + 0.045/1)^(1*4)
A = 3000(1.045)^4
A ≈ $3,434.31
Therefore, Adam is correct. Putting the money in the bank for four years at an interest rate of 4.5% will result in a higher total amount of money. Adam's investment will yield approximately $3,434.31, while Dawson's investment will yield approximately $3,428.52.
Dawson:
Principal amount = $3,000
Time = 2.5 years
Interest rate = 5.5%
The formula to calculate the compound interest is A = P(1 + r/n)^(nt), where:
A = the future value of the investment
P = the principal amount
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Applying the formula, we have:
A = 3000(1 + 0.055/1)^(1*2.5)
A = 3000(1.055)^(2.5)
A ≈ $3,428.52
Adam:
Principal amount = $3,000
Time = 4 years
Interest rate = 4.5%
Applying the same formula:
A = 3000(1 + 0.045/1)^(1*4)
A = 3000(1.045)^4
A ≈ $3,434.31
Therefore, Adam is correct. Putting the money in the bank for four years at an interest rate of 4.5% will result in a higher total amount of money. Adam's investment will yield approximately $3,434.31, while Dawson's investment will yield approximately $3,428.52.