CK-12-Pre-Calculus Concepts

13.2. Compound Interest per Year http://www.ck12.org

Compute the amount ending in an account for years 1, 2, 3 and 4 for an initial deposit of $100 at 3% compound
interest.
Solution: PV= 100 ,i= 0. 03 ,t= 1 , 2 , 3 and 4 ,FV=?

TABLE13.3:

Year Amount ending in Account

1 FV= 100 ( 1 + 0. 03 ) = 103. 00

2 FV= 100 ( 1 + 0. 03 )^2 = 106. 09

3 FV= 100 ( 1 + 0. 03 )^3 ≈ 109. 27

4 FV= 100 ( 1 + 0. 03 )^4 ≈ 112. 55

Calculator shortcut: When doing repeated calculations that are just 1.03 times the result of the previous calculation,
use the button to create an entry that looks like <Ans*1.03>. Then, pressing enter repeatedly will rerun the
previous entry producing the values on the right.
Example B
How much will Kyle have in a savings account if he saves $3,000 at 4% compound interest for 10 years?
Solution:
PV= 3 , 000 ,i= 0. 04 ,t= 10 years,FV=?

FV=PV( 1 +i)t

FV= 3000 ( 1 + 0. 04 )^10 ≈$4, 440. 73

Example C
How long will it take money to double if it is in an account earning 8% compound interest?
Estimation Solution: The rule of 72 is an informal means of estimating how long it takes money to double. It
is useful because it is a calculation that can be done mentally that can yield surprisingly accurate results. This can
be very helpful when doing complex problems to check and see if answers are reasonable. The rule simply states 72
i ≈t whereiis written as an integer (i.e. 8% would just be 8).
In this case^728 = 9 ≈t, so it will take about 9 years.
Exact Solution: Since there is no initial value you are just looking for some amount to double. You can choose
any amount for the present value and double it to get the future value even though specific numbers are not stated in
the problem. Here you should choose 100 forPVand 200 forFV.
PV= 100 ,FV= 200 ,i= 0. 08 ,t=?

FV=PV( 1 +i)t

200 = 100 ( 1 + 0. 08 )t

2 = 1. 08 t

ln 2=ln 1. 08 t

ln 2=t·ln 1. 08

t=ln 1ln 2. 08 = 9. 00646