Question

United Bank offers a 15-year mortgage at an APR of 6.2%. Capitol Bank offers a 25-year mortgage at an APR of 6.5%. Marcy wants to borrow $120,000.

a. What would the monthly payment be from United Bank?

b. What would the total interest be from United Bank? Round to the nearest ten dollars.

c. What would the monthly payment be from Capitol Bank?

d. What would the total interest be from Capitol Bank? Round to the nearest ten dollars.

e. Which bank has the lower total interest, and by how much?

f. What is the difference in the monthly payments?

g. How many years of payments do you avoid if you decide to take out the shorter mortgage?

Answer 1

a. To calculate the monthly payment from United Bank, we need to use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where M is the monthly payment, P is the principal amount, i is the monthly interest rate, and n is the number of monthly payments.

For United Bank, the principal amount is $120,000, the monthly interest rate is 6.2% / 12 = 0.00517, and the number of monthly payments is 15 years x 12 months/year = 180 months.

Plugging these values into the formula, we get:

M = 120000 [ 0.00517(1 + 0.00517)^180 ] / [ (1 + 0.00517)^180 – 1] = $1,011.25

Therefore, the monthly payment from United Bank is $1,011.25.

b. To calculate the total interest from United Bank, we can multiply the monthly payment by the number of payments and subtract the principal amount. The total interest is:

Total interest = M x n - P = $1,011.25 x 180 - $120,000 = $82,025

Therefore, the total interest from United Bank is $82,025.

c. To calculate the monthly payment from Capitol Bank, we can use the same formula as above. For Capitol Bank, the principal amount is $120,000, the monthly interest rate is 6.5% / 12 = 0.00542, and the number of monthly payments is 25 years x 12 months/year = 300 months.

Plugging these values into the formula, we get:

M = 120000 [ 0.00542(1 + 0.00542)^300 ] / [ (1 + 0.00542)^300 – 1] = $782.49

Therefore, the monthly payment from Capitol Bank is $782.49.

d. To calculate the total interest from Capitol Bank, we can use the same method as above. The total interest is:

Total interest = M x n - P = $782.49 x 300 - $120,000 = $154,747

Therefore, the total interest from Capitol Bank is $154,747.

e. United Bank has the lower total interest, by $72,722.

f. The difference in the monthly payments is $1,011.25

Answer 2

a. To calculate the monthly payment for the 15-year mortgage from United Bank, we can use the formula for the monthly payment on a mortgage:

```
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
```

where M is the monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate (which is the annual percentage rate divided by 12), and n is the total number of payments (which is the number of years multiplied by 12).

Plugging in the values we get:

```
P = $120,000
r = 6.2% / 12 = 0.00517
n = 15 * 12 = 180
```

So the monthly payment from United Bank would be:

```
M = $1,004.62
```

b. To calculate the total interest paid on the United Bank mortgage, we can multiply the monthly payment by the total number of payments and subtract the principal.

```
Total Interest = M * n - P
```

Plugging in the values we get:

```
Total Interest = $1,004.62 * 180 - $120,000 = $80,831.60
```

Rounding to the nearest ten dollars, the total interest from United Bank is $80,830.

c. To calculate the monthly payment for the 25-year mortgage from Capitol Bank, we can use the same formula as before.

```
P = $120,000
r = 6.5% / 12 = 0.00542
n = 25 * 12 = 300
```

So the monthly payment from Capitol Bank would be:

```
M = $760.03
```

d. To calculate the total interest paid on the Capitol Bank mortgage, we can use the same formula as before.

```
Total Interest = M * n - P
```

Plugging in the values we get:

```
Total Interest = $760.03 * 300 - $120,000 = $228,009.00
```

Rounding to the nearest ten dollars, the total interest from Capitol Bank is $228,010.

e. Capitol Bank has the higher total interest by $147,179.

f. The difference in monthly payments is $244.59.

g. The difference in years of payments is 10 years.