Question

The Johnsons 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. the second is a 20-year loan for a $150,000 at an interest rate of 3.9% APR compounded monthly. what is the total amount the Johnsons will pay by the end of the 20-year loan and by the end of the 30-year loan?

Answer 1

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

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

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

∴ $A=150,000(1+\frac{0.041}{12})^{(12)(30)}$

∴ 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

∴ $A=150,000(1+\frac{0.039}{12})^{(12)(20)}$

∴ A = $326,807.25

Johnson's will pay by the end of the 20-year loan $326,807.25

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