Tutorial 3 Interest Formulas SEEM 2510 Management Principles

Tutorial 3 Interest Formulas SEEM 2510 Management Principles for Engineering Managers II

“Effective” VS “Equivalent” ¡ ¡ ¡ Effective interest rate: rate of interest when compounding occurs more often than once a year. Effective interest rate effective interest rate MUST BE expressed in a yearly basic in this course

“Effective” VS “Equivalent” ¡ ¡ ¡ Equivalent interest rate: can be monthly and daily interest rates 8% compounded quarterly is equivalent to 8. 08% compounded semiannually Given a scheme with interest rate 15% compounded monthly. What is its equivalent interest rate for quarterly discrete compounding scheme?

Annual Percentage Rate (APR): ¡ ¡ ¡ Include the transaction costs Is given for reference according to the Code of Banking Practice in Hong Kong. In Hong Kong, APR means annual effective rate of interest.

Interest Formulas

Linear Gradient Series ¡ ¡ Constant increment: G First non-zero cash flow: period 2 G<0: decreasing gradient series G>0: increasing gradient series

Linear Gradient Series

Linear Gradient Series G (F/G, i, N) = G (F/A, i, N-1) + G (F/A, i, N-2) + G (F/A, i, N-3) +. . . + G (F/A, i, 2) + G (F/A, i, 1) (F/G, i, N) = (F/A, i, N-1) + (F/A, i, N-2) + (F/A, i, N-3) +. . . + (F/A, i, 3) + (F/A, i, 2) + (F/A, i, 1)

Linear Gradient Series ¡ The factors for the uniform gradient series:

Exercise 1 ¡ Use the formulas for the uniform gradient series and equal payment series to compute the future value.

Exercise 2 ¡ Suppose that the expenses are: $5, 000 for the second year, $6, 000 for the third year , $7, 000 for the forth year and , $8, 000 for the fifth year. ¡ What is the present worth of the expenses? Assume that the interest rate is 15%. ¡

Exercise 3 ¡ ¡ ¡ A local dealer is advertising a 24 -month lease of a sport utility vehicle for $520 payable at the beginning of each month. The lease requires a $2, 500 down payment, plus a $500 refundable security deposit. As an alternative, the company offers a 24 -month lease with a single up-front payment of $12, 780, plus a $500 refundable security deposit. The security deposit will be refunded at the end of the 24 -month lease. Assuming you have access to a deposit account that pays an interest rate of 6% compounded monthly, which lease is more favorable?

Exercise 4 ¡ Georgi Rostov deposits $5, 000 in a savings account that pays 6% interest compounded monthly. ¡ Three years later, he deposits $4, 000. ¡ Two years after the $4, 000 deposit, he makes another deposit in the amount of $2, 500. ¡ Four years after the $2, 500 deposit, half of the accumulated funds is transferred to a fund that pays 8% interest compounded quarterly. ¡ How much money will be in each account six years after the transfer?

Reference ¡ Chan S. Park, Fundamentals of Engineering Economics. Prentice Hall