If the rate of interest in Example 2 was 6% instead of 1.2%, how much will the account have after 24 months?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.4: Geometric Sequences And Series
Problem 7SC
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If the rate of interest in Example 2 was 6% instead of 1.2%, how much will the account have after 24
months?
Answer = $
(Round to the nearest penny)
%3D
Transcribed Image Text:If the rate of interest in Example 2 was 6% instead of 1.2%, how much will the account have after 24 months? Answer = $ (Round to the nearest penny) %3D
A certificate of deposit (CD) is a type of savings account offered by banks, typically
offering a higher interest rate in return for a fixed length of time you will leave your
money invested. If a bank offers a 24 month CD with an annual interest rate of 1.2%
compounded monthly, how much will a $1000 investment grow to over those 24
months?
First, we must notice that the interest rate is an annual rate, but is compounded monthly,
meaning interest is calculated and added to the account monthly.
188 Chapter 5
To find the monthly interest rate, we divide the annual rate of 1.2% by 12 since there
are 12 months in a year: 1.2%/12 = 0.1%. Each month we will earn 0.1% interest.
From this, we can set up an exponential function, with our initial amount of $1000 and a
growth rate ofr=0.001, and our input m measured in months.
m
.012
f (m) = 1000| 1+
12
f (m) = 1000(1+ 0.001)"
After 24 months, the account will have grown to f(24)=1000(1+0.001) = $1024.28
%3D
Transcribed Image Text:A certificate of deposit (CD) is a type of savings account offered by banks, typically offering a higher interest rate in return for a fixed length of time you will leave your money invested. If a bank offers a 24 month CD with an annual interest rate of 1.2% compounded monthly, how much will a $1000 investment grow to over those 24 months? First, we must notice that the interest rate is an annual rate, but is compounded monthly, meaning interest is calculated and added to the account monthly. 188 Chapter 5 To find the monthly interest rate, we divide the annual rate of 1.2% by 12 since there are 12 months in a year: 1.2%/12 = 0.1%. Each month we will earn 0.1% interest. From this, we can set up an exponential function, with our initial amount of $1000 and a growth rate ofr=0.001, and our input m measured in months. m .012 f (m) = 1000| 1+ 12 f (m) = 1000(1+ 0.001)" After 24 months, the account will have grown to f(24)=1000(1+0.001) = $1024.28 %3D
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