http://www.ck12.org Chapter 13. Finance
Example C
How much will Peter need to save each month if he wants to buy an $8,000 car with cash in 5 years? He can earn a
nominal interest rate of 12% compounded monthly.
Solution:In this situation you will do all calculations in months instead of years. An adjustment in the interest rate
and the time is required and the answer needs to be clearly interpreted at the end.
FV= 8 , 000 ,R=?,i=^012.^12 = 0. 01 ,n= 5 · 12 = 60
FV=R·(^1 +i)n− 1
i
8 , 000 =R·(^1 +^0.^01 )(^60) − 1
0. 01
R=( 18 +,^0000. 01 ·)^060.^01 − 1 ≈ 97. 96
Peter will need to save about $97.96 every month.
Concept Problem Revisited
Sally wanted to know how much she will have if she can earn 6% in a retirement account and she decides to save
$1,500 from her paycheck every month.
FV=?,i=^012.^06 = 0. 005 ,n= 30 · 12 = 360 ,R= 1 , 500
FV=R·(^1 +i)
n− 1
i
FV= 1 , 500 ·(^1 +^0.^005 )
(^360) − 1
0. 005
FV≈ 1 , 506 , 772. 56
Vocabulary
Anannuityis a series of equal payments that occur periodically.
Guided Practice
At the end of each quarter, Fermin makes a $200 deposit into a mutual fund. If his investment earns 8.1% interest
compounded quarterly, what will his annuity be worth in 15 years?
What interest rate compounded semi-annually is required to grow a $25 semi-annual payment to $500 in 8 years?
How many years will it take to save $1,000 if Maria saves $20 every month at a 5% monthly interest rate?
Answers:
Quarterly means 4 times per year.
FV=?,R= 200 ,i=^0.^0814 ,n= 60
FV= 200 ·(^1 +
(^0814) )^60 − 1
0814 ≈$23,^008.^71
2.FV= 500 ,R= 25 ,n= 16 ,i=?
500 = 25 ·(^1 +i)i^16 −^1 or 0 = 500 − 25 ·(^1 +i)i^16 −^1