Math 155 - CooleyFinite Math with Applications OCC
Sections 5.2 & 5.3 – Review
Formula Sheet for Annuity’s, Amortization, & Sinking Fund
Future Value of an Annuity
Monthly/Periodic payment is known & Future Value is unknown.
Present Value of an Annuity
Monthly/Periodic payment is known & Present Value is unknown.
Amortization Formula
Present Value of loan is known & Monthly/Periodic payment is unknown.
Sinking Fund
Future Value is known & Monthly/Periodic payment is unknown.
For all formulas above and .
S = amount after t years, future value
P = initial amount, present value
r = rate
m = number of times compounded per year
n = total number of times compounded over the entire period
R = monthly/periodic payment
Exercises: (Do all work on a separate sheet of paper)
1)Patrick just got a new job, and he immediately set up a tax-deferred annuity to save for his retirement.
He arranged to have $200 taken out of each of his monthly checks, which will earn % interest.
Patrick just had histhirtieth birthday, and his ordinary annuity will come to term when he is sixty-five.
Find the future value of theannuity. How much of the future value is interest?
2)Matt and Maria want to set up a sinking fund to save for their new baby’s college education. How much
wouldthey have to have deducted from their bi-monthly paycheck in order to have $30,000 in 18 years,
at % interest?
3)Cleo buys a new car for $16,113.82. She puts 10% down and obtains a simple interest amortized loan
for thebalance at % interest for 4 years. Find her monthly payment. Find the total interest.
4)Find the present value of an ordinary annuity that has $200 monthly payments for 25 years if the
account receives% interest.
5)Colin buys a car for $13,518.77. He makes a $1,000 down payment and finances the balance through
a 4-year simple interest amortized loan from his bank. He is charged 12% interest. Find the size of his
monthlypayment. Find the total interest for the loan.
6)Erica recently set up a TDA to save for her retirement. She arranged to have $290 taken out of each of
hermonthly checks; it will earn 11% interest. She just had her forty-fifth birthday, and her ordinary
annuity comes to term when she is sixty-five. Find the future value of the account. Find Erica’s total
contribution to the account.Findthe total interest.
7)Find the present value of an ordinary annuity that has $175 bi-monthly payments for 5 years if the
account receives % interest.
8)Scotty wants to save $1,200 over the next two years to use as a down payment on a new car. If
his bank offers him 9% interest, what monthly payment would he need to put into an ordinary annuity in
order to reach hisgoal?
Solutions to Exercises:
1) $552,539.96 , $468,539.96; 2) $27.09; 3) $378.35 , $3658.36; 4) $21,182.36;
5) $329.67 , $3,305.39; 6) $251,035.03 , $69,600.00 , $181,435.03; 7) $18,177.57; 8) $45.82
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