Question

1. What is the future value at the end of year 18 of $10,000 deposited today into an account that pays interest of 4.5% p.a., but with daily compounding (assume 365 days per year)?

2. Ellie is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $11,500; year 2, $10,000; year 3, $7,500; year 4, $5,000; year 5, $2,500; year 6, $0; and year 7, $12,500. Ellie believes that she should earn an annual rate of 8 percent on this investment. How much should Ellie pay for this investment?

 

Answer 1

Answer to Question 1:

Amount Deposited = $10,000
Time Period = 18 years or 6,570 days

Annual Interest Rate = 4.50%

Daily Interest Rate = (1 + Annual Interest Rate)^(1/365) - 1
Daily Interest Rate = (1 + 0.0450)^(1/365) - 1
Daily Interest Rate = 1.0001206 - 1
Daily Interest Rate = 0.0001206 or 0.01206%

Future Value = Amount Deposited * (1 + Daily Interest Rate)^Time Period
Future Value = $10,000 * 1.0001206^6,570
Future Value = $10,000 * 2.208457
Future Value = $22,084.57

Answer to Question 2:

Rate of Return = 8%

Cash Flow:
Year 1 = $11,500
Year 2 = $10,000
Year 3 = $7,500
Year 4 = $5,000
Year 5 = $2,500
Year 6 = $0
Year 7 = $12,500

Present Value = $11,500/1.08 + $10,000/1.08^2 + $7,500/1.08^3 + $5,000/1.08^4 + $2,500/1.08^5 + $0/1.08^6 + $12,500/1.08^7
Present Value = $37,845.52