Math OER
Week 2 Homework, Part B

1. Brenda can afford to spend $900 per month on mortgage payments (and dealing with a downpayment) and wants a 30-year loan. Currently mortgage rates are 5% per year. Use the amortization table to find what price home can she afford.

$48,000 $60,000 $150,000 $168,000

2. Brenda gets a loan with a 25% downpayment. What will be the size of Brenda's actual mortgage and monthly payment?

$67,000 mortgage and $356.12 monthly payment
$126,000 mortgage and $675.36 monthly payment
$168,000 mortgage and $900.00 monthly payment
$210,000 mortgage and $1,125.60 monthly payment

3. Brenda's loan has a 2% mortgage fee, first month pre-paid, and $1,000 other up-front costs. What is the total of her downpayment and these other up-front costs?

$46,195 $46,420 $47,035 $47,260

4. Zane has an annual income of $65,000. He wants to spend 30% of his income on a mortgage, with a 15-year loan. The interest rate is 5%. Use the amortization table to find what price home can he afford.

$205,000 $216,000 $246,000 $260,000

5. Zane gets a loan with a 15% downpayment. What will be the size of his actual mortgage and monthly payment?

$162,000 mortgage and $1,281.42 monthly payment
$174,250 mortgage and $1,378.32 monthly payment
$183,600 mortgage and $1,452.28 monthly payment
$205,000 mortgage and $1,625.00 monthly payment

6. Zane's loan has a 4% mortgage fee, first month pre-paid, and $1,300 other up-front costs. What is the total of his downpayment and these other up-front costs?

$37,642 $40,398 $41,872 $43,345

Switching to saving for retirement...

7. Use the end-of-monthly increasing annuity formula to find what a $15 monthly deposit would become after 40 years at 4% annual interest.

$45 $5,890 $4,500 $17,730 $64,070

The End-of-Monthly Increasing Annuity Formula

Final Amount = Deposit × [ (1 + monthly rate)^{number of months}    −    1] ÷ monthly rate

Remember to divide the annual rate by 12 to find the monthly rate.

Recall that at the end of this week's earlier homework assignment we discovered what would happen if someone invested $3,865 for 40 years with 9% annual compound interest. Those numbers were chosen because of Vanguard's research showing that the average 25-year-old American has saved $3,865 for retirement, and the average 65-year-old American has saved $176,696.

Now you can see why you found out how much less than $176,696 was the answer to that compound interest problem. You were answering the question, "How much has the average 65-year-old American saved beyond simply letting that youthful $3,865 grow with average stock market income?"

Sadly, the answer is "not much".

8. Fiddle around using the end-of-monthly increasing annuity formula to find what monthly deposit would grow to $176,696 over 40 years at 9% annual interest. (Hint: an annual deposit of $33 is too small, but $46 is too big.)

$35.36 $37.74 $41.12 $45.24

This is sad. You just found an equivalent to what the average 65-year-old American saved each month for 40 years, if they knew how to invest. Such a small amount. ☹ It is easy to be above average!

On another note, how does the long-term financial cost of infant care compare to saving for kids' college expenses?

9. The "big three" child care centers in Eugene cost roughly $1,080 per month. Imagine a family instead saves that money each month a 5% annual interest rate. Use the end-of-monthly increasing annuity formula for 24 months (when the infant is age 1 and 2) and carefully find only the interest earned.

$112.87 $1,280.79 $2,164.50 $3,755.13

10. Continuing the previous problem, take the $27,200.79 total amount that the family had at the end of those 24 months and allow it to compound monthly for sixteen years (until the child is 18) at a 5% annual interest rate. Use the compound interest formula to find how much could be saved towards the child's college tuition.

$28,560.83 $29,071.97 $60,435.95 $318,366.24

Short Answer Question: Show your work for using the Decreasing Annuity Formula to solve problems #1 and #4 without the amortization table.

The Decreasing Annuity Formula (aka Amortization or Payout Annuity)

Principal = Withdrawl × [ 1  −  (1 + rate per payout)^{− number of payouts} ] ÷ rate per payout