Suppose n(U) = 150, n(A) = 35, and n(B) = 89. (a) If n(A U B) = 90, find n(A n B).
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Johnson's will pay by the end of the 20-year loan $326,807.25
Johnson's will pay by the end of the 30-year loan $512,109.68
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
The Johnson's are buying their first home. They are contemplating
two similar loans
The first is a 30-year loan for $150,000 at an interest rate of 4.1% APT
compounded monthly
∴ P = $150,000
∴ r = 4.1% = (4.1/100) = 0.041
∴ n = 12 ⇒ compounded monthly
∴ t = 30
- Substitute all of these values in the formula above
∴
∴ A = $512,109.68
Johnson's will pay by the end of the 30-year loan $512,109.68
The second is a 20-year loan for a $150,000 at an interest rate of 3.9%
APR compounded monthly
∴ P = $150,000
∴ r = 3.9% = (3.9/100) = 0.039
∴ n = 12 ⇒ compounded monthly
∴ t = 20
- Substitute all of these values in the formula above
∴
∴ A = $326,807.25
Johnson's will pay by the end of the 20-year loan $326,807.25
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