FIN 301: HW 5

A loan is offered with monthly payments and a 9.50 percent APR. What's the loan's effective annual rate (EAR)?

EAR=[1+(0.0950/12)]^12−1 =0.0992=9.92%

Compute the future value in year 8 of a $3,200 deposit in year 1, and another $2,700 deposit at the end of year 3 using a 10 percent interest rate.

FV8 = $3,200 × (1 + 0.10)^7 + $2,700 × (1 + 0.10)^5 = $6,235.89 + $4,348.38 = $10,584.27. Or N = 7, I = 10, PV = −3,200, PMT = 0, CPT FV == 6,235.89 and N = 5, I = 10, PV = −2,700, PMT = 0, CPT FV == 4,348.38 then $6,235.89 + $4,348.38 = $10,584.27.

What is the future value of a $800 annuity payment over six years if interest rates are 10 percent?

FVA6=$800×(1+0.10)^6−1/0.10 =$800×7.7156=$6,172.49 Or N = 6, I = 10, PV = 0, PMT = −800, CPT FV == 6,172.49

Monica has decided that she wants to build enough retirement wealth that, if invested at 8 percent per year, will provide her with $5,000 of monthly income for 20 years. To date, she has saved nothing, but she still has 25 years until she retires. How much money does she need to contribute per month to reach her goal? First compute how much money she will need at retirement, then compute the monthly contribution to reach that goal.

First, calculate the amount you would need to have in 25 years time to yield the $5,000 monthly payments for an additional 20 years. PVA= $5,000×[1−(1/(1+0.08/12)^240/(0.08/12))]=$597,771.46 Or N = 20 × 12, I = 8/12, PMT = −5,000, FV = 0, CPT PV = 597,771.46 This amount will become the future value in the next calculation, assuming 8 percent interest and 300 level monthly payments. $597,771.46=PMT×(1+0.08/12)^300−1(0.08/12)⇒PMT =$628.55 Or N = 25 × 12, I = 8/12, PV = 0, FV = 597,771.46, CPT PMT = −628.55

Create the amortization schedule for a loan of $10,500, paid monthly over three years using an APR of 8 percent. Enter the data for the first three months.

PMT36=$10,500×[(0.08/12)1−(1(1+0.08/12)^36)]=$329.03 Beginning balance = 10500.00, 10240.67, 9980.21 Total Payment = 329.03 Interest Paid = 70.00, 68.27, 66.53 Principal Paid = 259.03, 260.76, 262.50 Ending Balance = 10240.97, 9980.21, 9717.71

You wish to buy a $26,500 car. The dealer offers you a 4-year loan with a 10.8 percent APR. What are the monthly payments? How would the payment differ if you paid interest only?

PMT48=$26,500×[(0.108/12)1−(1(1+0.108/12)^48)] =$26,500×0.025748504 =$682.34 Or N = 4 × 12, I = 10.8/12, PV = 26,500, FV = 0, CPT PMT = −682.34 If you only paid interest over the length of the loan and your principal balance was repaid at the end of the 48 months, your payment would be $238.50 per month (= $26,500 × 0.108 ÷ 12) for interest only and you would owe $26,500 at the end of the 48 months, too.

You wish to buy a $25,500 car. The dealer offers you a 5-year loan with a 9 percent APR. What are the monthly payments? How would the payment differ if you paid interest only?

PMT60=$25,500×[(0.090/12)/1−(1(1+0.090/12)^60)] =$25,500×0.020758355=$529.34 Or N = 5 × 12, I = 9.0/12, PV = 25,500, FV = 0, CPT PMT = −529.34 If you only paid interest over the length of the loan and your principal balance was repaid at the end of the 60 months, your payment would be $191.25 per month (= $25,500 × 0.090 ÷ 12) for interest only and you would owe $25,500 at the end of the 60 months, too.

Given a 7 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,350, $1,550, $1,550, and $1,850, respectively.

PV = $1,350 ÷ (1 + 0.07)^1 + $1,550 ÷ (1 + 0.07)^2 + $1,550 ÷ (1 + 0.07)^3 + $1,850 ÷ (1 + 0.07)^4 PV= $1,261.68 + $1,353.83 + $1,265.26 + $1,411.36 = $5,292.13 Or N = 1, I = 7, PMT = 0, FV = −1,350, CPT PV == 1,261.68and N = 2, I = 7, PMT = 0, FV = −1,550, CPT PV == 1,353.83and N = 3, I = 7, PMT = 0, FV = −1,550, CPT PV == 1,265.26and N = 4, I = 7, PMT = 0, FV = −1,850, CPT PV == 1,411.36 Then sum the PVs = $1,261.68 + $1,353.83 + $1,265.26 + $1,411.36 = $5,292.13.

Compute the present value of a $2,900 deposit in year 1, and another $2,400 deposit at the end of year 3 if interest rates are 10 percent.

PV = $2,900 ÷ (1 + 0.10)^1 + $2,400 ÷ (1 + 0.10)^3 = $2,636.36 + $1,803.16 = $4,439.52. Or N = 1, I = 10, PMT = 0, FV = −2,900, CPT PV == 2,636.36 and N = 3, I = 10, PV = −2,400, PMT = 0, CPT FV == 1,803.16 then $2,636.36 + $1,803.16 = $4,439.52.

What's the present value, when interest rates are 8.0 percent, of a $75 payment made every year forever?

PV of a perpetuity=$75/0.080=$937.50

You are looking to buy a car. You can afford $440 in monthly payments for four years. In addition to the loan, you can make a $1,100 down payment. If interest rates are 7.25 percent APR, what price of car can you afford (loan plus down payment)?

PVA48=$440×[1−(1/(1+0.0725/12)^48)/(0.0725/12)]+$1,100=$18,285.79+$1,100 =$19,385.79 Or N = 4 × 12, I = 7.25/12, PMT = −440, FV = 0, CPT PV == 18,285.79Add the down payment of $1,100 to get $19,385.79.

What's the present value of a $610 annuity payment over six years if interest rates are 10 percent?

PVA6=$610×[1−(1/(1+0.10)^6/0.10)] =$610×4.355261=$2,656.71 Or N = 6, I = 10, PMT = −610, FV = 0, CPT PV == 2,656.71