Question

1. You and your spouse have found your dream home. The selling price is $220,000; you will put $50,000 down and obtain a 30-year fixed-rate mortgage at 12% compounded monthly for the balance a) Assume that monthly payments begin in one month. What will each payment be? b) How much interest will you pay (in dollars) over the lifetime of the loan? (Assume you make each of the required 360 payments on time.) c) Although you will get a 30-year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in 20 years? 2. Mr. And Mrs. James would like to need $30,000 per year during their retirement periods to have a comfortable life. They assume that they will retire in 20 years and expect a 15-year retirement period. They will be able to eam 10% per year during the 15 years retirement period. a) How large a fund will they need when they retire in 20 years to provide the 15-year, $30,000 retirement annuity? b) How much will they need today as a single amount to provide the fund calculated in part a if they earn 8% per year during the 20 years retirement period?

Answer 1

1.Selling price=	220000
Less:Down pmt.=	50000
Loan amt.	170000

a. To find out the equal monthly payment:

using the present value of ordinary (period-end) annuity formula

PV of loan=Pmt.*(1-(1+r)^-n)/r

where,

PV of loan , we have as , 170000

pmt.=the mthly.pmt.---to be found out

r= the mthly.interest rate,ie. 12%/12=1% or 0.01

n= no.of pmt. Periods= 30 yrs. *12 mths.= 360 months

so, now, plugging these values in the formula,

170000=Pmt.*(1-1.01^-360)/0.01

solving the above, we get the mthly.pmt. As

170000/((1-1.01^-360)/0.01)=

1748.64

Each payment will be $ 1748.64

b. Total Interest payment on the loan=

Amt.paid towards interest=Total mthly pmts.-the principal loan amt.

(1748.64*360)-170000=

459510.40

c. If you, wish to pay-off the loan in 20 yrs.,ie. n= 20 yr. *12= 240 months

the additional pmt. Reqd. can be calculated as:

170000=(1748.64+x)*(1-1.01^-240)/0.01

Solving for x, we get the addl. Pmt. As

$123.21

2..The amt. of fund they will need when they retire at end 20 yrs./beg. Yr.21 ,

for 15 yrs. To provide $ 30000 annuity will be

the present value of year-end annuity of $ 30000

at r= 10%, for a period of n= 15

so,using the PV of ordinary annuity formula,

PV of the fund=retirement annuity*(1-(1+r)^-n)/r

& plugging the above values,

PV=30000*(1-1.1^-15)/0.1

228182.39

This is the future value of the

single sum at timt t=0

that earns r=8% p.a.

for a period of n= 20 yrs.

so, using the FV of a single sum formula,

FV=PV*(1+r)^n

& plugging the above values,

228182.39=PV*(1+0.08)^20=

Solving the above,

we get the single sum today as

228182.39/(1+0.08)^20=

48956.12