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
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.