3. (a) Twenty years ago, Ain gave birth to a baby boy named Aiman. During that time, she decided to open an investment account that gave a return of 6.5% compounded monthly. She invested $50 every month in the account for her son as a preparation for his education. Today, Aiman receive an offer to study in a university for 4 years. Ain transfer the account to Aiman for him to use the money for his education expenses.

(i) What is the amount in the account when the account is transferred to Aiman?

(ii) How much should Aiman withdraw every month so that he will have enough money until he completes his studies? (3 marks) (b) Lukman borrowed $75 000 from Tenaga Bank that charged interest of 7.65% compounded monthly. He paid $1 508 every month for 5 years. However, after the 36th of payment, he decided to settle his remaining debt in single payment at 37th payment. How much is the total payment he made at the 37th?

FORMULA 1. Inverse, A-1 = A 2. Cramer's Rule, Xi Ail |A| Where: A; is a matrix obtain by replacing ith column of A by the vector B 3. I = Prt 4. S=P+I=P(1 + rt) 5. S= P(1+i)" (1+i)" - 1 S = R 6. 7. r = (1 + )m - 1 8. Interest charged based on reducing balance: Annuity Method A= R 1-(1+i)" i where A= i = n = the amount of loan borrowed the interest rate per interest period the number of interest periods or the number of instalment repayment monthly payment or instalmen payment for each period R= 9. Interest charged based on reducing balance: Annuity Method ((1+i)n R[(1+0)-1] i where S= n = the amount of annuity the interest rate per interest period the number of interest periods or the number of instalment repayment the periodic payment R= 10. Markup = Selling Price (Retail Price) Cost or M=SP-C 11. Selling Price = Cost + Operating Expenses + Net Profit or SP=C+ OE + NP 12. Breakeven Price = Cost + Operating Expenses or BEP=C+ OE 13. Original balance = Cash price - Down payment or OB =CP-DP 14. Periodic payment = (Original balance+Interest)/(Number of payment) R=(OB+1) 15. Installment price = Cash price + Interest = Original balance + down payment + Interest = Down payment + total periodic payment 16. I = B(n+1) 2M 17. OPB = Rk - 1 [k(k+1) In(n+1)