Question

HINT{pls provide with all formulas and solutions}

What etlect does compounding interest more frequently than any have on (al Nuture values and b) the cffective annual rate (EARJE Why [4 mars DJ Jason DOROM RM15.000 from a bank an 10 percent annually compounded interest to be repeta in sk equal Instatments Calculate the interest paid in the second year (4 marks) al suppose you want to buy a house years from now. The average price of your dream house k RM500.000 and its price is growing at 5 porcent per year. To accumulate enough money to buy your dream house with cash at the end of the ninth year, how much will you deposit into an account at the end of every year paying annual Interest of 12 (4 marios oh Ranakts 30 years old and he has decided that it is the time to plan for his retirement at age of 65. He expects a 15-year retirement period and concluded that he would need RM25.000 per year during his retirement years in order to lve comfortably. How much should Razak saves ct the end of each year in an account paying Interest per annum to meet his goal at age of 653 (4 mares) e Last Decembet Attor rocolved an amud bonus of RM1 500. These annual bonusos oro expected to grow by 5 percent annually for the next 5 years. How much will Amor have at the end of the film year it he invests annual bonuses finching the most recent bonus in a project paying 8 percent per year

Answer 1

A Compounding interest more frequently will have higher futute value and higher effective annual rate as compared to compounding interest annualy.This is because in compound interest we gets interest on interest and higher the frequency of compounding more number of times interest will be calculated with a year. For example interest compounded annualy will get interest only once on invested amount, interest compounded semi annualy will get interest on invested amount as well as on first 6 months earned interst. NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN b Installment = Principal Loan Amount Annuity factor Since Interest is compounded annualy, effective interest rate = 10% Annuity Factor = (1-1/(1+r)^n)/r = (1-1/1.10^6)/.10 = (1-1/1.7716)/.10 = (1-0..5645)/.10 = 0.4355/.10 4.355 Installment = 15000/4.355 = 3444.32 1 2 3 4 Installment o/s Loan Interest Principal Repaid 3444.32 15000.00 1500.00 1944.32 3444.32 13055.68 1305.57 2138.75 3444.32 10916.93 1091.69 2352.63 3444.32 8564.30 856.43 2587.89 3444.32 5976.41 597.64 2846.68 3444.32 3129.73 312.97 3131.35 5 6 Interest paid in the secind year is $1305.57 NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN

c Furture price of house = Current price(1+r)^5 - 500000(1.05)^5 638140.7813 Installment = Future value [(1+r)^n-1)/r 638141 (1+.12)^5-1)/.12 638141 (1.7623-1)/.12 638141 6.3525 100455.10 Annual amount to be deposited = 100455.10 NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN d Retirement Corpus = 25000x15 375000 Time to invest 35 years Rate of Interest 6% Annual Savings = Retirement corpus ((1+r)^n-1)]/r 375000 (1+.06)^35-1)/.06 375000 (7.6861-1)/.06

11 375000 (6.6861)/0.12 375000 55.7175 6730.38 Annual amount to be deposited = 6730.38 NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN e Year 1 2 Bonus 1,500.00 1,575.00 1,653.75 1,736.44 1,823.26 3 FV Factor Bonus + Interest 1.47 2,203.99 1.36 2,142.77 1.26 2,083.25 1.17 2,025.38 1.08 1,969.12 10,424.51 4 5 Amount at the end of 5 years = 10424.51