Section 4.1
What interest is calculated by applying the interest rate to the principal only, not to interest earned?
The largest monthly payment you can afford is $300. Can you afford to borrow a principal of $8000 with a term of 2 years?
So, your monthly payment will be at least $333.34 which is more than you can afford.
A(n) _________________is an arrangement that withdraws bot principal and interest from your nest egg.
A perpetuity is an arrangement that withdraws only interest from your nest egg.
An annuity is an arrangement that withdraws bot principal and interest from your nest egg.
You have a credit card with an APR of 19.7%.
You begin with a balance of $1200 and in response make a payment of $300. The first month you make charges amounting to $200.
Find the finance charge for month 1. Round to the nearest cent.
As a borrower, you are searching for the lowest possible rate. Which of the following options is the best deal for a borrower?
A) 3.25% compounded semiannually
B) 3.25% compounded quarterly
C) 3.25% simple interest
To purchase a home, you take out a mortgage for $150,000. Your outstanding balance after 40 payments is about $138,745. What is your equity on your home after forty payments?
If you borrow money to pay for an item, your equity in that item at a given time is the part of the principal you have paid.
150,000-138,745= $11,255
Calculate the following:
500 × ((1+.04/12)^120 - 1)
divided by
.04/12
Round to two decimal places.
Numerator: 245.4163412...
Denominator: .0033333333333....
Computation: 73,624.90
You have a credit card with an APR of 19.7%.
You begin month 2 with a previous balance of $1118.06 and in response make a payment of $400. This month you make charges amounting to $500 and have a finance charge of $20.00.
What is your New Balance?
As an investor, you are searching for the highest possible rate.Which of the following options will help you earn the most interest?
A) 3.24% compounded simiannually
B) 3.23% compounded monthly
C) 3.21% compounded daily
B) 3.23% compounded monthly has an APY of
(1+.0323/12)^12 - 1 = .032782491 or about 3.278%
This is higher than the other APYs.
You find that the going rate for a home mortgage with a term of 30 years is 7.6% APR.
If your largest monthly payment is $800, how much can you borrow?
Amount borrowed =
(Monthly payment × ((1+r)^t-1) )/((r(1+r)^t ) )
Monthly payment = $800 r = .076/12 t = 360
Amount borrowed is calculated to be $113,302.5
This means you can afford to borrow $113,302.50
How much do you need to deposit each month for three years into a savings account that pays 6.5% APR in order to buy a car that costs $25,000?
Answer: $630.81
Use formula: Needed deposit =(Goal × r )/
((1+r)^t-1)
r = .065/12 t = 36 Goal = 25,000You have a balance of $10,000 for your tuition on your credit card and you make no further charges. If your APR is 20% and each month you make only the minimum payment of 4.5% of your balance, what will be your balance after 24 months?
10000((1+.2/12)(1-.045))24 = $4,924.55
Suppose you invest $5000 in a savings account that pays an APR of 4%. If the interest is compounded monthly, what is the balance in the account after 10 years?
A = P(1+r)^t. P = 5000 r=.04/12 t = 12X10 = 120
A = $7454.16
Suppose you borrow $350,000 for a 30-year mortgage and have found an APR of 6% compounded monthly. The monthly payment is calculated to be $2098.43. Assuming you pay off the mortgage on time, what will be the total amount paid? How much interest will be paid?
Total amount paid = 360 X 2098.43 = $755,434.80
Interest paid =
$755,434.80 - $350,000 = $405,434.80
You have set up a life annuity with a present value of $250,000. If your life expectancy at retirement is 25 years, what will your monthly income be if the APR is 8%, compounded monthly.
Answer: $1929.54
Use formula: Monthly annuity yield = (Nest egg × r(1+r)^t )/((1+r)^t-1)
Nest egg = 250,000, r = .08/12, t = 25X12 = 300
You have a balance of $600 on your credit card and make no more charges. Assume the card carries an APR of 16%. Suppose you want to pay off the card in one year by making equal payments each month. What is your monthly payment?
Use the following formula from 4.2: Monthly payment = (Amount borrowed × r(1+r)^t )/((1+r)^t-1)
Amount borrowed = 600 r = .16/12 t = 12
Monthly payment = $54.44
What is the present value of an investment that will be worth $5000 at the end of ten years assuming an APR of 8% compounded monthly?
A = P(1+r)^t A = 5000, t = 12X10, r = .08/12
P = $2252.62
To buy a car, you borrow $25,000 with a term of three years at an APR of 6.5%. Your monthly payment is $766.23.
What part of your first payment is "applied to interest"?
What part of your first payment is "applied to balance owed"
After making that first payment, what is your "outstanding balance"?
Part of first payment that is "applied to interest" =
(.065/12) = $135.42
Part of first payment that is "applied to balance owed" = $766.23 - $135.42 = $630.81
New Outstanding Balance = $25,000 - $630.81 =$24,369.19
Explain how you would solve the following problem. Be sure to note what formulas you would use and what you would substitute in for the variables.
You plan to retire in 40 years. How much would you need to deposit each month into a savings account with an APR of 6% compounded monthly if your goal is to have a monthly annuity yield also with an APR of 6% of $500 per month for 20 years.
First use the 4.3 "Nest Egg Needed" formula to find the nest egg you would need to fund your annuity yield goal of $500 per month.
Annuity yield goal = 500, r = .005 t = 20X12=240
Second , use the 4.3 "Needed Deposit" formula. Substitute your "Nest Egg Needed" for "Goal" and solve for "Needed Deposit".
Goal = solution from first formula r=.005 t = 40X12= 480
You have a balance of $10,000 for your tuition on your credit card and you make no further charges. If your APR is 18.9% and each month you make only the minimum payment of 3.5% of your balance, Then the balance after t payments = 10000(0.98019875)t
Determine when the balance would be less than $50. Round your answer to the nearest month.
50 = 10000(0.98019875)t
Divide both sides by 10000
.005 = (0.98019875)t
log(.005) = log((0.98019875)t)
log(.005) = tlog(0.98019875)
log(.005)/log(0.98019875) = t
264.9.....or about 265 months.