Jenny wants to give her 14-year-old daughter $20,000 when she turns 18. How much does she need to put in the bank now if the int
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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:
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 = $258,223.20
If it paying in 24 years
∴
∴ 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 = $223,328.17
If it paying in 24 years
∴
∴ 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
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The amount of money spent by these persons individually will be $ 93, $116, and $ 99.
<h3>What is the matrix?</h3>A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.
Ram, Shyam, and Mohan purchased biscuits from different brands P, Q, and R.
Ram purchased 10 packets of P, 7 packets of Q, and 3 packets of R.
Shyam purchased 4 packets of P, 8 packets of Q, and 10 packets of R.
Mohan purchased 4 packets of P, 7 packets of Q, and 8 packets of R.
If brand P costs € 4, Q costs € 5, and R costs € 6 each.
Then the amount of money spent by these persons individually will be
Then these are shown in the form of a matrix. Then we have
Then the amount of money spent by these persons individually will be
More about the matrix link is given below.
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