You are taking out a student loan to pay for college. For a Federal...

Question

# You are taking out a student loan to pay for college. For a Federal...

You are taking out a student loan to pay for college.
For a Federal student loan in 2022-2023, the interest rate is 4.99%, compounded monthly.
1. If you want to pay the loan off by paying \$250 each month, for 10 years, how much can
you afford to borrow?
2. If you borrow \$29,000, how much will you need to pay back each month to pay the loan
back in 10 years?
Use this information for problems 3 and 4. You borrow \$12,000 for a home repair. You can
afford to pay back \$350 a month.
3. If you borrow the money directly from a bank, you have a 7.25% interest rate. How long
will it take you to pay off the loan?
4. If you borrow the money using a credit card, you will have a 21.85% interest rate. How
long will it take you to pay off the loan?
Use this information for problems 5 and 6. You are looking to buy a house with a 30-year
mortgage. The interest rate is 6.875%.
5. You find a house which costs \$200,000.
a. What will your monthly payments be?
b. How much will you end up paying total for the house?
6. You look at another house which costs \$300,000.
b. How much will you end up paying total for the house?
c. How much more did you end up paying for the \$300,000 house?
7. You will often hear people talking about buying a house when interest rates are low.
Repeat your calculations from problem 5 (the \$200,000 house) if the interest rate were
4.5% instead. Is there a big difference in the monthly payments and how much you end
up paying total?

8. In each case, identify the formula (simple interest, compound interest, annuity, payout
annuity/loan) you would use to solve the problem. Explain why you chose that formula.
You do not need to solve the problem. You will not receive full credit if you do not
explain why you chose the formula.
a. Bernice saved money to live off of while they do a 3 year trip around the world.
If they have \$100,000 saved in an account that pays 4.5% interest, compounded
monthly, how much can they afford to take out each month?
b. Tony bought a used car for \$12,000. If they borrowed the money at 4.5%
interest for 3 years, what will their payments be each month?
c. Dina has a credit card which charges 19.5% interest, compounded monthly. If
they put \$3000 on the card, how much will they need to pay each month to pay
the card off in 6 months?
d. Andre borrows \$1200 to repair their car. If the loan charges 12% interest,
compounded daily, and they pay it back 6 months later, how much will they
need to pay?
e. Artemis is saving up for a trip around the world. They want to save \$200 each
month for 2 years. What interest rate, compounded monthly, do they need to
have if they want to save \$6000?

For problems 8-10, state the correct formula (simple interest, compound interest, annuity, or
payout annuity/loan) and the variable in the formula that you need to solve for. Explain why
you made those choices. Then solve the problem.
9. Rhonda borrows \$12500 at 7.45% interest, compounded monthly. They pay the money
back in monthly payments, paying \$200 each month. How long does it take them to pay
the money back?
10. Felipe wants to save \$2 million dollars for retirement. If they have the money in an
account which pays 8% interest, and they have 20 years until retirement, how much
they need to save each year?

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