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2 years ago

Dan took out a 24-year loan for $111,000 at an APR of 7.7%, compounded

Mathematics

2 answers:

Gekata [30.6K]2 years ago

7 0

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:

$A=P(1+\frac{r}{n})^{nt}$ 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

∴ $A=111,000(1+\frac{0.077}{12})^{(12)(11)}$

∴ A = $258,223.20

If it paying in 24 years

∴ $A=111,000(1+\frac{0.077}{12})^{(12)(24)}$

∴ 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

∴ $A=96,000(1+\frac{0.077}{12})^{(12)(11)}$

∴ A = $223,328.17

If it paying in 24 years

∴ $A=96,000(1+\frac{0.077}{12})^{(12)(24)}$

∴ 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

#LearnwithBrainly

dem82 [27]2 years ago

3 0

Dan would save more, since he has $15,000 more in principal.

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