Question

PART 2: FINANCE

a) What is the most that you would pay for an investment that promises to pay $20,258.00 a year forever with the first payment starting one year from now? Assume that your required rate of return for this investment 23.70%.

b) A loan has a stated annual rate of 6.55%. If loan payments are made monthly and interest is compounded monthly, what is the effective annual rate of interest?

c) You invest $2134.00 at the beginning of every year and your friend invests $2134.00 at the end of every year. If you both earn an annual rate of return of 12.56%, how much more money will you have after 12 years?

d) You currently have $1784.00 in a retirement savings account that earns an annual return of 6.00%. You want to retire in 47 years with $1,000,000. How much more do you need to save at the end of every year to reach your retirement goal?

e) You currently owe $3206.00 of your credit card that charges an annual interest rate of 18.70%. You make $136 of new charges every month and make a payment of $215 every month. What will your credit card balance be in three months?

Answer 1

a. Amount that you would pay for the investment=

Present value at t=0 of the annual year-end perpetuity of $ 20258 at an interest rate of 23.70 % p.a.

Formula to be used is

PV of investment=CF1/r

ie. 20258/23.70%=

85476.79

So, the answer is

Amount that you would pay for the investment= $ 85476.79

b.Effective annual rate=(1+(Annual rate/No.of compounding periods)^(No.of compounding periods in a year)-1

here, it is EAR=(1+(r/12))^12-1

ie. (1+(6.55%/12))^12-1

6.75%

(Answer)

c. Future value of Beginning-of-yr. investments=

FVAdue =(Pmt.*((1+r)^n-1)/r)*(1+r)

ie.(2134*((1+12.56%)^12-1)/12.56%)*(1+12.56%)=

59979.45

Future value of end-of-yr. investments=

FVOA =(Pmt.*((1+r)^n-1)/r)

ie.(2134*((1+12.56%)^12-1)/12.56%)=

53286.65

FVAdue-FVOA=

59979.45-53286.65=

6692.80

Answer is:

You will have $ 6692.80 more than your friends after 12 yrs.

d.That is

FV of a single sum of 1784 at end of 47 yrs.PLUS FV of year-end annuities for 47 yrs. should equal $ 1000000---both at 6% p.a.

(1784*1.06^47)+(pmt.*(1.06^47-1)/0.06)=1000000

solving for pmt., we get the amount you need to save at the end of every year to reach your retirement goal, as

$4,033.24

(Answer)

e.
Month	New charges	Int.amt.	Pmt. Made	O/s bal.
1	2	3=Prev.5*18.70%/12	4	5=Prev.5+2+3-4
0				3206
1	136	49.96	215	3176.96
2	136	49.51	215	3147.47
3	136	49.05	215	3117.52

the answer is:

your credit card balance in three months=

3117.52