Respuesta :
Dan would save more by paying off his loan 13 years early
Step-by-step explanation:
The formula for compound interest, including principal sum, is:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] where:
- A is the future value of the investment/loan, including interest
- P is the principal investment amount (the initial deposit or loan amount)
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per unit t
- t is the time the money is invested or borrowed for
Dan took out a 24-year loan for $111,000 at an APR of 7.7%,
compounded monthly
∴ P = $111,000
∴ r = 7.7% = (7.7/100) = 0.077
∴ n = 12 ⇒ compounded monthly
∵ The loan is paid in 13 years
∴ t = 24 - 13 = 11 years ⇒ 13 years early
- Substitute these values in the formula above
∴ [tex]A=111,000(1+\frac{0.077}{12})^{(12)(11)}[/tex]
∴ A = $258,223.20
If it paying in 24 years
∴ [tex]A=111,000(1+\frac{0.077}{12})^{(12)(24)}[/tex]
∴ A = $700,382.38
∴ Dan saves = 700,382.38 - 258,223.20 = $442,159.18
Forrest took out a 24-year loan for $96,000 at an APR of 7.7%,
compounded monthly
∴ P = $96,000
∴ r = 7.7% = (7.7/100) = 0.077
∴ n = 12 ⇒ compounded monthly
∵ The loan is paid in 13 years
∴ t = 24 - 13 = 11 years ⇒ 13 years early
- Substitute these values in the formula above
∴ [tex]A=96,000(1+\frac{0.077}{12})^{(12)(11)}[/tex]
∴ A = $223,328.17
If it paying in 24 years
∴ [tex]A=96,000(1+\frac{0.077}{12})^{(12)(24)}[/tex]
∴ A = $605,736.11
∴ Forrest saves = 605,736.11 - $223,328.17 = $382.407.94
∵ Dan saves $442,159.18
∵ Forrest saves $382,407.94
∴ Dan would save more by paying off his loan 13 years early
Dan would save more by paying off his loan 13 years early
Learn more:
You can learn more about interest in brainly.com/question/8280736
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