1). What is the present value of an ordinary annuity that pays $1200 a month for
ID: 2637096 • Letter: 1
Question
1). What is the present value of an ordinary annuity that pays $1200 a month for 5 years at 7.8%
compounded monthly? (SHOW WORK)...Round answer to the nearest cent.
2). A family takes out a 30-year, $200,000 mortgage at 4.20% compounded monthly after putting $50,000 down to buy a home valued at $250,000 ($50,000 is 20% of $250,000). Find:
a. the monthly payment is $978.034 a month (I figured this out on my own...)
b. the unpaid balance after 16 years? (SHOW WORK)
c. the equity the family has built up in its house after 23 years of monthly payments, if the
house
Explanation / Answer
1>PV of Annuity when A=1200 , n=5 Year and i=7.8% p.a. Interest per month=0.078/12 0.0065 Interest Factor=(1+0.0065)^(5*12) 1.475 PV=1200*(F-1)/F*i=1200*(1.475-1)/(1.475*0.0065) 59452.41 2>Monthly Interest=4.2/12 0.35 Interest Factor=(1+0.0035)^(12*30) 3.52 a>Capital Recovery per month=A=200000*(F*i)/(F-1)=200000*(3.52*0.0035)/(3.52-1) 977.78 b>Balance after 16years=200000-977.78*12*16 12266.24 c>Amount paid in 23years=977.78*12*23 269867.3 Equity=310000-269867.3 40132.7
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