1) You Are Considering Buying a New Car. the Sticker Price Is $20,000 and You Have $2,000

FI3300 – Fall 2007

Exam Two

1) You are considering buying a new car. The sticker price is $20,000 and you have $2,000 to put toward a down payment. If you can negotiate a nominal annual interest rate of 12 percent and you wish to pay for the car over a 5-year period, what is your monthly car payment?

A. 264.18

B. 400.40

C. 789.25

D. 1593.01

E. 2446.93

Amount of loan = 20,000 – 2,000 = 18,000

The loan is a monthly payment loan. Therefore adjust the nominal interest rate and no. of payment periods.

Periodic interest rate = 12/12 = 1%

Number of periods = 5 x 12 = 60

PV = 18000, FV = 0, I/Y = 1, N = 60. Then CPT, and PMT.

PMT = -400.40

2) What is the present value of a security that pays $900 per year for 10 years (with the first payment to be made today and the last payment to be made 9 years from today) given an interest rate of 5.75 percent p.a.?

A. 6721.34

B. 6955.02

C. 7088.68

D 7376.67

E 123.05

This is an annuity due. So use the relationship between an ordinary annuity and an annuity due to find the present value.

Find present value of the corresponding ordinary annuity.

PMT = -900, N = 10, I/Y = 5.75, FV = 0. Then CPT and PV.

PV = 6,703.2482

Therefore, present value of the annuity due = 6,703.2482 x (1.0575) = 7,088.684972

So final answer (to 2 decimal places) = $7,088.68

3) You plan to deposit $150 every month for 22 years (with the first deposit made one month from today) into an account that pays 6 percent p.a. What is the future value of this annuity at the end of year 30 ?

A 149,070.23

B 132,252.98

C 95,360.02

D 81,933.88

E 77,512.95

No. of periods = 22 x 12 = 264

Periodic interest rate, (what you put into I/Y) = 6/12 = 0.5%

N = 264, I/Y = 0.5, PMT = -150, PV = 0. Then CPT and FV = 81,933.8801

Now, move your focus to the end of year 22 and make that your starting point. You want to find the future value of 81,933.8801 at the end of year 30.

No. of periods between the end of year 30 and the end of year 22 = ( 30 – 22 ) x 12 = 96

Key in the following to get the future value of 81,933.8801 at the end of year 32.

N = 96, PV = -81,933.8801, I/Y = 0.5, PMT = 0. Then CPT and FV = 132,252.98

4) Ira Longview wishes to save money to provide for his retirement. Beginning one year from now, he will deposit the same fixed amount each year for the next 20 years into a retirement savings account. Starting one year after making his final deposit, he will withdraw $135,000 annually for each of the following 15 years (i.e. he will make 15 withdrawals in all). Assume that the retirement fund earns 6% annually over both the period that he is depositing money and the period he makes withdrawals. In order for Ira to have sufficient funds in his account to fund his retirement, how much should he deposit annually?

A 15,856.39

B 21,270.34

C 35,643.13

D 325,875.02

E 1,088,192.94

There are two annuities.

Annuity 1: Deryl deposits fixed annual amounts for 20 years into the retirement savings account.

Annuity 2: Deryl withdraws money for 15 years.

Find PV of Annuity 2 at the end of year 20.

FV = 0, N = 15, I/Y = 6, PMT = 135,000. Then CPT and PV.

PV = -$1,311,153.6130

Use the PV of Annuity 2 at the end of year 20 as the FV which Deryl must accumulate by making deposits into the retirement savings accounts.

Find annual deposit into retirement savings accounts.

FV = $1,311,153.6130, PV = 0, I/Y = 6, N = 20. Then CPT and PMT.

PMT = -$35,643.13

15) You have borrowed $11,500 from a bank and have promised to repay the loan in 10 equal yearly payments. The first payment is at the end of the first year. The interest rate is 5 percent p.a.. How much interest will you pay at the 6th payment?

A 286.33

B 296.45

C 322.39

D 343.16

E 405.55

PV=11500, N=10, I/Y=5, FV=0, PMT=-1489.30,

PUSH key on the BAII Plus, 2ND and AMORT, input p1=6, p2=6, will find the interest amount.