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1

Finance Oct 02, 2020

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. 

Expert Solution

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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