Mathematics in Finance

The formula:

TUTORIAL 8 : SIMPLE INTEREST AND SIMPLE DISCOUNT 1. Rosli deposited RM7000 in a bank and obtained RM140 as a simple interest after three months. Find the simple interest rate offered. 2. Rahman invested RM5000 at 4.5% simple interest in a bank. Find the amount in his account after six months. 3. Miss Yan deposited RM8000 in a bank and obtained simple interest of RM600 after 3 years. What was the simple interest offered? ii. How much interest could she earn if she deposited RM20000 in the bank for eight months? 4. Hidayah invested RMQ in a bank. Her investment is worth RM7500 after 36 months. If the simple interest rate is 9% per annum, find the value of Q. 5. Five years ago , Man invested RM8800 in a bank at a simple rate of 7.2% per annum. Find i. the amount of his account today ii. the number of years required if Man wanted RM12601.60 to be the amount in his account. 6. Tan borrowed RM10000 for 100 days at 9% per annum simple interest. i. How much is the interest charged? ii. What is the amount owed and the end of 100 days? (Use the Banker's Rule : 1 year=360 days) Answers : 1) 8% 2) RM5112.50 3) 2.5% , RM333.33 4) RM5905.51 5) RM11968, 6 years 6) RM250, RM10,2507. Find the proceeds of RM12000 due in 2 years at a simple discount 12%. 8. If Amoi needs RM15000, how much should she borrow from the bank for 3 years at 9% discount rate. 9. What discount rate a lender should charge in order to earn an interest rate of 15% per annum on a one-year loan? 10. Lim borrowed RM30000 for 2 years at a simple discount rate of d%. He received RM27000 as proceeds. Find the value of discount rate d. 11. How much money Ali borrowed if he was given 5% discount rate for 6 months and received proceeds of RM1950. 12. A businessman needs RM12000 for four months. What should the loan size be if the bank charges a discount rate of 9.5%. Answers : 7) RM9120 8) RM20547.95 9) 13.04% 10) 5% 11) RM2000 12) RM12392.43SIMPLE INTEREST The interest calculated on the original principal for the entire period it is borrowed or invested. I = Prt where I =simple interest P =principal r =rate of simple interest t =time/term in yearsBank discount, D is computed on the final amount or maturity value. D = Sdt where D =bank discount S =amount of maturity value d =discount rate t =term of discount in years Bank Proceeds, P =Maturity value - Bank discount P =S - D P = S - SdtSimple Interest Rate Equivalent to Bank Discount Rate Let r% is an interest rate and d% is discount rate. If the two rates give the same present value for an amount due in the future : both rate are said to be equivalent : if the amount is S, then the present value of S at r% simple interest rate is S - AND 1+rt at d% bank discount rate is S(1 - dt)1. A debt of RM600 is due in three years and RM800 due in four years is to be repaid by a single payment two years from now. If the interest rate is 8% semiannually, how much is the payment? [6 marks] 2. A debt of RM5000 due in five years is to be repaid by a payment of RM2000 now and the second payment at the end of six years. How much should the second payment be if the interest rate is 6% quarterly. [6 marks] 3. A debt of RM5000 due five years from now and RM5000 due ten years from now is to be repaid by a payment of RM2000 in two years, a payment of RM4000 in four years and the final payment at the end of six years. If the interest rate is 7% annually, how much is the final payment? [8 marks]