Question 2 (a) RM 250 is invested every month in an account that pays monthly fo

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Question 2 (a) RM 250 is invested every month in an account that pays monthly for two years. After the two years, no more deposits are m the amount of the account at the end of the five years. compounded ade. Find 896 (5 marks) (b) Serena invests RM 300 every months for four years. She is offered 5% compounded quarterly for the first two years and 8% compounded quarterly for the rest of the period. Find the accumulated amount at the end of the four years. (5 marks) Raihan has to pay RM300 every month for 24 months to settle a loan at 12% compounded monthly, what is the original value of the loan? (c) (5 marks) Johan won an annuity that pays RM 1,000 every three months for 3 years. What is the present value of this annuity if the money is worth 16% compounded quarterly. (d)

Explanation / Answer

a) An amount R= RM 250, is deposied every mont, for t= 2 years, at an interest rate i = 8%.

So at the end of the first year, the amount that has accumulated in the account is the future value of the monthly annuity of RM 250 8% for 24 months = S= R(((1+i)n - 1)/i) = 250(((1+0.08)24 - 1)/0.08) = RM 16,691.19

The amount S is with the bank for the next 3 years = 36 months, which gives us a return of 8% per month. Therefore the amount in the bank at the end of the fifth year = S' = S(1+i)n = 16691.19(1.08)36 = RM 2,66.527.787,

b) An amount R= RM 300, is deposited every month, for t= 4 years, at an interest rate i1 = 5% (quarterly) = 5%/3 = 1.67% (monthly) for the 1st two years and i2 = 8% (quarterly) = 8/3 =2.67% (monthly)

So at the end of the first year, the amount that has accumulateded in the account is the future value of the monthly annuity of RM 300 1.67% for 24 months = S= R(((1+i1)n - 1)/i1) = 300(((1+0.0167)24 - 1)/0.0167) = RM 8768

The amount S is with the bank for the next 2 years and the deposits R also continuos for the next two years = 24 months, which gives us a return of 2.67% per month. Therefore the amount in the bank at the end of the fourth year is the sum of the future value of S and monthly deposits R at 2.67% interest rate.

Therefore, S' = S(1+i2)n +  R(((1+i2)n - 1)/i2)= 8768(1.0267)24 + 300(((1+0.0267)24 - 1)/0.0267)

= 16502.36+9911.37

= RM 26413.73

c) Monthly installment of RM 300, has to be paid against the loan at an interest rate of 12% monthly for 24 months.

The original loan amount here is the present value of the annuity, A with R = RM 300, i = 12%, n=24

therefore, A = R(1-(1+i)-n)/i

= 300((1-(1+0.12)-24 )/0.12)

=RM 2335.30

Therefore the loan amount is around RM 2335.30.

d) Annuity pay R = Rm 1000 for every 3 months(quarterly), for n = 3 years = 36 months = 12 quarters. The quarterly interest rate = 16%

Thus the present value of the annuity = A = R(1-(1+i)-n)/i = 1000 (1-(1+0.16)-12)/0.16 = RM 5197.11

Therefore the present value of the annuity is RM 5197.11

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