Question

Suppose you invested $5,000 in a CD on January 1, 2015 maturing in 20 years that pays interest of 4% per year compounded semiannually and credited at the end of each six month period. You don't withdraw any money from the CD during its term.

(a) How much money was in the CD account on July 1, 2015?

b) How much money was in the CD account on January 1, 2016?

(c) How much money will be in the CD account on January 1, 2025?

(d) What is the total amount of interest paid on the CD during these 10 years?

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

(f) When will the money in the CD account first be $10,000 or greater?

Answer 1

(a) money in the CD account on July 1, 2015 = amount deposited*(1+semi-annual interest rate)no. of semi-annual periods

money in the CD account on July 1, 2015 = $5,000*(1+0.04/2)1 = $5,000*(1+0.02) = $5,000*1.02 = $5,100‬

(b) money in the CD account on January 1, 2016 = $5,000*(1+0.04/2)2 = $5,000*(1+0.02)2 = $5,000*1.022 = $5,000‬*1.0404‬ = $5,202‬

(c) money in the CD account on January 1, 2025 = $5,000*(1+0.04/2)20 = $5,000*(1+0.02)20 = $5,000*1.0220 = $5,000‬*1.4859473959783543420355740092833‬‬ = $7,429.74

(d) total amount of interest paid on the CD during these 10 years = money in the CD account on January 1, 2025 - initial deposit = $7,429.74 - $5,000 = $2,429.74‬