Question

3. Suppose you invest $20,000 in a CD on January 1, 2020 maturing in 14 years that pays interest of 5% per year compounded semiannually (meaning every six months) and credited at the end of each six month period. You don't withdraw any money from the CD during the term.

(a) How much money is in the CD account on July 1, 2020?

(b) How much money is in the CD account on January 1, 2021?

(c) How much money will be in the CD account when it matures, namely 14 years after January 1, 2020?

(d) What is the total amount of interest paid on the CD during these 14 years?

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

(f) When will the money in the CD account first be $30,000 or greater?

Answer 1

a

FV = PV ( 1+r)^n

Where n is Int rate per period
n - No. of periods

FV = 20000(1+0.025)^1

= 20000(1.025)^1

= $ 20500

b

FV = 20000(1+0.025)^2

  = 20000(1.025)^2

= 20000 * 1.05063

= $ 21012.6

c

FV = 20000(1+0.025)^28

= 20000(1.025)^28

= 20000 * 1.9965

= 39930

d

Maturity value - 20000

= 39930-20000

= $ 19930

e

EAR = (1+r)^n-1

= (1+0.025)^2-1

= 1.025^2 -1

= 1.05063 -1

= 0.050603

i.e., 5.06 %

f

FV = PV ( 1+r)^n

30000 = 20000 (1+0.025)^n

30000 / 20000 = 1.025^n

1.5 = 1.025^n

take log on both sides

Log(1.5) = Log (1.025^n)

0.1761 = n * log 1.025

0.1761 = n * 0.0107

n = 0.1761 / 0.0107

n = 16.46

no of years = 16.46/2 = 8.23 years

after 8.23 years the money in CD account first be $ 30000 or greater.

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