Question

1) (3 pts) Bob would like to have a total savings of $30,000 in 6 years to use as a down payment on a future house purchase. He has no money saved up now, but plans on depositing $350 per month at the end of every month to save for this goal. What is the periodic interest rate Bob must earn to reach his goal? What is the Annual Percentage rate? 1 Periodic *.ㅡ I Nominal (APR)- % 2) (3 pts) Sue currently has $40,000 to use as a down payment on a house and can afford to pay $950 per month for a mortgage. If the interest rate on a 30-year mortgage is 6.0% (this is an APR) compounded monthly. What is the highest price house she can afford to purchase today using a 30-year mortgage? (2 pts) Larry would like to retire in 25 years. He currently has $150,000 in his retirement account and is planning on depositing an additional $800 each month in his retirement account. If Larry can earn an average APR of 7% per year compounded monthly. how much money will be in his retirement account after 25 years? 3) (2 pts) You want to set up an endowed scholarship that will pay $5000 a year in perpetuity. If the appropriate interest rate is 4% compounded annually, how much will you have to donate today to set up the endowed scholarship? 4) (2 pts) You want to buy a $24,000 car and have saved up $3,000 to use as a down payment. If you finance the remaining cost of the car at 4.2% (APR) compounded monthly for 5 years, what will your monthly payment be? 5)

Answer 1

Total savings required after 6 years = $30,000

Period = 6 years = 72 months

Deposits he can make = pmt = $350

To find 1.periodic interest rate   2. annual percentage rate

Formula FV = PMT*((1+r)ⁿ-1)/(r) where FV is the value he want to save

PMT is monthly he can save

n = 72 months

The value of R calculated is periodic and when multiplied by 12 will give annual rate

Solving the above equation

30000 = (350*(1+r)⁶-1)/(r)

periodic r = 0.478%

annual r =5.74%