Section 2-3 FV of an Annuity; Sinking Funds
Goal: To calculate future values of annuities and solve problems involving sinking
funds
Any sequence of payments at equal time intervals is called an annuity.
To calculate the future value of an annuity:
  r nt 
 1    1
 n 

,
FV  PMT  
r
n
where FV = future value ($)
PMT = periodic payment ($)
r = annual interest rate (as a decimal)
t = time in years
and n = number of payments per year (periods)
If the payments into an account are in the form of an ordinary annuity and the account is established for
accumulating funds to meet a future obligation, then the account is called a sinking fund.
(Unless otherwise noted, round monetary answers to the nearest dollar, precents to two
decimal places when written as a percentage, and time to the nearest year.)
1. Annual deposits of $2,500 are made for 15 years into an annuity that pays 6.25%
compounded annually. Find 𝑖 (the rate per period) and 𝑛 (the number of
periods) for each annuity.
i = 0.065; n = 15
2. USG Annuity and Life offered an annuity that pays 6.95% compounded
monthly. If $800 is deposited into this annuity every month, how much is in the
account after 12 years? How much of this is interest?
r = 0.0695 / 12 = 0.0058
PMT = 800
t = 12
n = 12
FV = 800 * ((1 + 0.0058/ 12)144 – 1) / (0.0058 / 12) = 119 273.77
Total payment = 800 * 12 * 12 = 115 200
Interest earned = 119 273.77 – 115 200 = 4 073.77
3. John wanted to save for his retirement but he procrastinates and does not make
his first $1,000 deposit into an IRA until he is 36, but then he continues to
deposit $1,000 each year until he is 65 (30 deposits in all). If John’s IRA also
earns 6.4% compounded annually, how much is in his IRA when he makes his
last deposit on his 65th birthday?
PMT = 1000
t = 30
r = 0.064
FV = 1000 * ((1 + 0.064)30 – 1) / (0.064) = 84852.51