The Amount of an Annuity

So far, all of our calculations have been based on the following concept: You deposit a certain amount of money, and leave it for years at a time, never saving any more (Lump Sum Savings)

Is this the only way people save money? Not at all…. Another more common way of savings, is to put aside smaller amounts whenever you can Since this is a more realistic way to save, we will spend most of our time examining this situation. This type of saving plan is called an annuity

An annuity is a series of equal payments made at regular intervals. (Think of a car payment: same amount at the end of each month…) The amount of the annuity is the sum of the regular deposits plus interest.

Consider this savings plan… You make regular deposits of $ into an account once a year for 10 years. The money will earn 6%.

A = R[(1 + i) n – 1] i The Amount of an Annuity formula: A - the amount in dollars R - the regular payments in dollars i - the interest rate, per cycle, as a decimal n - is the number of cycles

A = R[(1 + i) n – 1] i For our current question… A - ? R -$ i n -10

A = 1000[(1.06) 10 – 1] 0.06 For our current question… = 1000[0.7908] 0.06 = = $ For your homework, as long as you have the first substitution step, and the final answer correct, you will receive full marks…

Suppose you deposit $ every 6 months into an account at 4.5% compounded semi-annually. How much will you have after 3 years?

A = ?, R = A = R[(1 + i) n – 1] i 250, i =0.045 = n = 2 times a year for 3 years = 6 A = 250[( ) 6 – 1]

= 250 [0.1428] A = 250[( ) 6 – 1] = $

Consider your own savings… What if you saved just $25.00 per month… $25.00 / month at 4% (C:S-A), 40 years? (adjust the payments to 6 months 25 X 6 = 150, 4% / 2 = 2% = 0.02, and 6 months for 40 years is 80) A = 150[(1.02) 80 – 1] 0.02 = $ !!!

Pearson Pg , 6a,c 7,9,11,12