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1

Finance

1.You are negotiating a deal for the purchase of a new vehicle! The sticker price of the vehicle is $21,595. You mention you have a $400/mo budget. The dealer tells you he can give you a 60 month loan at an interest rate of 5.25% APR, with payments of ONLY $395.80!!! Round all answers to the nearest cent. a. What price is he offering for the vehicle? (equivalent cash payment): $ You respectfully decline this offer and offer to pay $20,000 for the vehicle (at 5.25%). b. What would that make the payments be? S The dealer has one final offer for you: $20,300 for the vehicle, only 2.5% APR. Is this a better than $20,000 at 5.25%APR? Option 1: $20,300 @ 2.5% APR Option 2: $20,000 @ 5.25% APR PMT. $ PMT. $ Total Paid: $ Total Paid: $ c. Which option is better?

2.Calculate the value of a bond that will mature in 18 years and has a ?$1,000 face value. The annual coupon interest rate is 15?percent, and the? investor's required rate of return is 12 percent.

3.Sarah Wiggum would like to make a single investment and have $2.5 million at the time of her retirement in 25 years. She has found a mutual fund that will earn 5 percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of 16 percent, how soon could she then retire? a. If Sarah can earn 5 percent annually for the next 25 years, the amount of money she will have to invest today is $ 738256.93. (Round to the nearest cent.) b. If Sarah can earn an annual return of 16 percent, the number of years until she could retire is years. 

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1.Calculation of price of vehicle;

Total cash payment = 395.8*60 = 23748 with interest rate per month of 5.25/12 = 0.4375%

Present value of payment gives cash price of the product

PV = 395.8* [1-(1+0.4375%)^-60]/0.4375% = 395.8*52.678 = 20850

Payment for 20000 at 5.25%

Equal monthly instalment = 20000/[PVAF at 0.4375%] = 20000/52.678 = 379.72

PVAF at 0.4375% calculated in previous step

Payment of 20,300 at 2.5%

=20300/[PVAF at 2.5/12%] = 20300/56.346 = 360.27

(PVAF at 2.5/12% = [1-(1+0.2083%)^-60]/0.2083% = 56.346)

This option provides lower outflow of cash per month and hence this is beneficial.

2.

Annual coupon=1000*15%=150

Hence value of bond=Annual coupon*Present value of annuity factor(12%,18)+1000*Present value of discounting factor(12%,18)

=150*7.24967008+1000*0.13003959

=$1217.49(Approx)

NOTE:

1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=150[1-(1.12)^-18]/0.12

=150*7.24967008

2.Present value of discounting factor=1000/1.12^18

=1000*0.13003959

3.

. Is correct. The Investment today=$738256.93

b. Use NPER function in EXCEL to find the number of years

=NPER(rate,pmt,pv,fv,type)

rate=16%

pmt=0

pv=738256.93

fv=2500000

type=0

=NPER(16%,0,-738256.93,2500000,0)=8.22

The retirement years comes to 8.22 years

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