Question

1. An annuity pays $10 per month for 50 years. What is the future value (FV) of this annuity at the end of that 50 years given that the interest rate is 5%?

2. Since your first birthday, your grandparents have been depositing $1000 into a savings account on every one of your birthdays. The account pays 4% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, what will be the amount of money in your savings account?

3. You are considering purchasing a new home. You will need to borrow $250,000 to purchase the home. A mortgage company offers you a 15-year fixed rate mortgage (180 months) at 9% annual rate. If you borrow the money from this mortgage company, what will be your monthly mortgage payment? Make the amortization plan for this loan.

4. You have just agreed to work for PriceWaterhouseCoopers as an external consultant for the next 6 years. In your contract you specified that in one year time Price will pay you $36,000 for your consultant services. For your services in the following three years you will receive $50,000 each year. Compensation for the last two years of your contract will be $60,000 per year. The opportunity cost of capital is 8%.

1. How much is your contract worth today?
2. If you decide to save the proceeds from your contract, how much will you have at the end of the 6^th year?

5. You are borrowing money to buy a car. If you can make payments of $300 per month starting one month from now at an interest rate of 4%, how much will you be able to borrow for the car today if you finance the amount over four years?

6. You are planning to borrow $100,000 on a 5-year to invest in your start-up firm. Interest rate stated by the bank is 9%. You plan to make payments quarterly. What will be your quarterly payment? Make an amortization plan for this loan.

Answer 1

1. This needs working ut the future value of ordinary annuity of

Pmt.= $10

at an interest rate , r= 5%/12=0.4167% or 0.004167p.m.

for n= 50*12= 600 months

Using the formula for FVOA & plugging in the above values,

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

ie. 10*((1+0.4167%)^600-1)/0.4167%=

26690.18

(Answer)

2.Formula to be used is

Future value of ordinary annuity

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

where,

FVOA-----needs to be found out----??

Pmt.= $ 1000 at end of yrs. 1 to 17

r= interest rate, 4% or 0.04 p.a.

n= no.of pmts.= 17

Using the above formula for FVOA & plugging in the above values,

ie.(1000*((1+0.04)^17-1)/0.04)

23697.51

(ANSWER)

Amount of money in your savings account, Immediately after your grandparents make the deposit on your 18th birthday = $ 23697.51

The mortgage amortisation table for 1st 10 pmts. Have been shown , as under ---due to space constraints-----in the answer tab

No.of mth.	Mthly.pmt.	Tow. Int.	Tow. Mortgage	Mortgage Bal.
0				250000
1	2535.7	1875	660.67	249339.33
2	2535.7	1870.045	665.625	248673.7
3	2535.7	1865.053	670.6172	248003.09
4	2535.7	1860.023	675.6468	247327.44
5	2535.7	1854.956	680.7142	246646.73
6	2535.7	1849.85	685.8195	245960.91
7	2535.7	1844.707	690.9632	245269.94
8	2535.7	1839.525	696.1454	244573.8
9	2535.7	1834.303	701.3665	243872.43
10	2535.7	1829.043	706.6268	243165.81

4..Contract's worth today

is the sum of the present values of all the amounts at 8% cost of capital

ie.(36000/(1+0.08)^1)+(50000/1.08^2)+(50000/1.08^3)+(50000/1.08^4)+(60000/1.08^5)+(60000/1.08^6)=

231288.55

If all the above are saved for end of Yr. 6,

we can direcly, find the Future of this single sum of $ 231288. 55 (PV at t=0) , at 8% per period , for 6 periods

ie. 231288.55*(1+0.08)^6=

367025.86

5. Amount you will be able to borrow for the car today

is the Present value of the end-of monthly payments of $ 300 p.m.

at r=4%/12=0.3333% or 0.0033 p.m.

for n= 4 yrs.*12= 48 no.of mthly. Pmts.

So, using the Present value of ordinary annuity

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

PVOA=300*(1-(1+0.0033)^-48)/0.0033=

13297.19

ie. The amount you will be able to borrow for the car today= $ 13297.19

6. Using the PV of ordinary annuity formula,

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

where, PVOA= $ 100000

Pmt.= the quarterly pmt.--to be found out----??

r= rateof interest per quarter, ie. 9%/4=0.0225 or 2.25% per qtr.

n= no.of pmt.- qtrs., ie. 5*4= 20

So, using the Present value of ordinary annuity formula,

100000=Pmt.*(1-(1+0.0225)^-20)/0.0225

The qtrly. Pmt.=100000/((1-(1+0.0225)^-20)/0.0225)

6264.21

The amortisation table is as follows

No.of Qtrs.	Qtrly. Pmt.	Tow. Int.	Tow. Loan	Loan Bal.
1	2	3=Prev. 5*2.25%	4=2-3	5=Prev. 5-Currrent 4
0				100000
1	6264.21	2250	4014.21	95985.79
2	6264.21	2159.68	4104.53	91881.26
3	6264.21	2067.33	4196.88	87684.38
4	6264.21	1972.90	4291.31	83393.07
5	6264.21	1876.34	4387.87	79005.20
6	6264.21	1777.62	4486.59	74518.61
7	6264.21	1676.67	4587.54	69931.07
8	6264.21	1573.45	4690.76	65240.31
9	6264.21	1467.91	4796.30	60444.00
10	6264.21	1359.99	4904.22	55539.78
11	6264.21	1249.65	5014.56	50525.22
12	6264.21	1136.82	5127.39	45397.83
13	6264.21	1021.45	5242.76	40155.07
14	6264.21	903.49	5360.72	34794.35
15	6264.21	782.87	5481.34	29313.01
16	6264.21	659.54	5604.67	23708.34
17	6264.21	533.44	5730.77	17977.57
18	6264.21	404.50	5859.71	12117.85
19	6264.21	272.65	5991.56	6126.30
20	6264.21	137.84	6126.37	-0.07
	125284.20	25284.13	100000.07