Question

A discounted Certificate of Deposit with a face value of USD 2.5 million issued for a period of 90 days at a rate of 3.5%.

1. Between the buyer and issuer, who receives and who parts with money

2. What is the price at which this CD is transacted?

3. The CD is sold 45 days later at a rate of 3.75%. What is the selling price? Explain the two components generating the difference with the first price found.

4. How much would the CD be worth if it was held until the day of its maturity and the rate for 90 days on that day would be 3.80%

Answer 1

Part 1) Buyer receives the CD & makes payment. Issuer will issue the CD & receives the money

Part 2) Assume number of days in a year = 360 days

Interest rate for 90 days = 3.5%*90/360 = 0.875%

Price at which CD is transacted = $2,500,000/(1+0.875%)

= $2,500,000/(1+0.00875) = $2,500,000/1.00875 = $2,478,315

Part 3) Assume number of days in a year = 360 days

Interest rate for 45 days = 3.75%*45/360 = 0.46875%

Selling price = $2,500,000/(1+0.46875%)

= $2,500,000/(1+0.0046875) = $2,500,000/1.0046875 = $2,488,336

Components genrating difference is Interest rate & period of CD.

If for example same 3.5% interest rate is maintained the price would be

Interest rate for 45 days = 3.5%*45/360 = 0.4375%

Price = $2,500,000/(1+0.4375%) = $2,500,000/(1+0.004375) = $2,500,000/1.004375 = $2,489,110

Difference due to interest rate = $2,489,110-$2,488,335=$774.

The CD which is near to maturity date, price will automatically increase as compared to issue price because on maturity date it will be equal to face value.

Part 4) Assume number of days in a year = 360 days, Assume held from 1st day till maturity

Interest rate for 90 days = 3.8%*90/360 = 0.95%

Price of the CD = $2,500,000/(1+0.95%)

= $2,500,000/(1+0.0095) = $2,500,000/1.0095 = $2,476,474.