Question

10. Suppose you invested $2,000 in a CD on January 1, 2016 maturing 5 years that pays interest of 4% per year compounded monthly and credited at the end of each month. You don't withdraw any money for the CD during the term.

(a.) How much money will be in the CD account on January 1, 2021?

(b.) What is the effective annual rate of interest on this CD?

Answer 1

a)In order to find our value of CD on januray 1, 2021 we will use formula:

C=P(1+r)^n

Where,

C=Future value

P=Principal=2000

r=ROI=4%/12=0.04/12 (Divided by 12 for monthly compounding)

n=No. of compounding periods=5*12=60 (Multiplied by 12 for monthly compounding)

Hence,

C=2000*[(1+(0.04/12))^60]

=2000*[(1+0.003333)^60]

=2000(1.22099659)

=$2,441.993

Thus, we will get $2,441.993 on January 1, 2021

b)effective annual rate=(1+i/n)^n-1

Where i=Annual ROI=4%=0.04

n=No. of compoundings per anum=12

putting in formula,

=(1+0.04/12)^12-1

=(1.003333)^12-1

=1.04074-1

=0.04074

=4.074%

Thus, effective annual rate is 4.074%

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