Here is the problem you need to solve:
- On a $250,000 mortgage amortized over 30 years (360 months) at an interest rate of 11%, what would be the monthly payment?
- On a $125,000 mortgage with monthly payments of $1,049.00 at an interest rate of 9%, what is the length of time this mortgage is amortized over?
- On a $100,000 mortgage amortized over 20 years (240 months) with monthly payments of $1,118.56, what would the interest rate be?
- If a mortgage is amortized over 30 years (360 months) at an interest rate of 10% and monthly payments of $2,632.71, what is the original value of the mortgage?
- If a mortgage is amortized over 30 years (360 payments) at a 9.5% interest rate for $150,000 and there is a balloon due in 15 years (180 payments), what would be the monthly payment amount and the balloon amount? (This is a two-part question.)
Here is the solution:
5. Part a., if a mortgage is amortized over 30 years (360 payments) at a 9.5% interest rate for $150,000 and there is a balloon due in 15 years (180 payments), what would be the monthly payment amount?
This part of the question is asking us what the monthly payment amount on this mortgage would be, therefore, we can conclude that we are solving for PMT on the first part of this example. The mortgage is amortized over 30 years, so we would enter 360 into N. The interest rate is 9.5%, so we would enter that into I. It’s a $150,000 mortgage, so we would enter that amount into PV. We don’t know what the balloon payment amount is yet, so, we would enter 0 into FV. The answer, as listed above, should be $-1,261.28.
5. Part b., if a mortgage is amortized over 30 years (360 payments) at a 9.5% interest rate for $150,000 and there is a balloon due in 15 years (180 payments), what would be the monthly payment amount and the balloon amount?
Now we are looking for the balloon amount on this mortgage, so, we would be solving for FV. All of the information in the above explanation remains the same in the second part of this example, except N. If the balloon is due in 15 years, we would change N to 180 and solve for FV. The answer, as listed above, should be $-120,786.39.
Lets look at this example further and let me explain what is happening here. In most mortgages that include a balloon payment, the monthly payments are usually amortized over a longer period of time then when the mortgage is actually due. In this example, the payments were amortized over 30 years, but the balloon payment is due in 15 years. This means that there are actually only 15 years worth of monthly payments or 180 monthly payments of $1,261.28, then, the balloon payment amount of $120,786.39 is due. Once that balloon payment is paid and the 180 monthly payments have been paid, the mortgage is paid off, there are no more payments left.
Here is the answers are listed in bold.
Example # |
N |
I |
PV |
PMT |
FV |
1. |
360 |
11% |
$250,000 |
$-2,380.81 |
0 |
2. |
300 |
9% |
$125,000 |
$-1,049.00 |
0 |
3. |
240 |
12.25% |
$100,000 |
$-1,118.56 |
0 |
4. |
360 |
10% |
$299,999.46 |
$-2,632.71 |
0 |
5.a. |
360 |
9.5% |
$150,000 |
$-1,261.28 |
0 |
5.b. |
180 |
9.5% |
$150,000 |
$-1,261.28 |
$-120,786.39 (Ans) |