Question

Question 1 Since she is moving to Bali after retirement, Ranjeeta decides to sell her house in Malaysia. The buyer is willing to pay RM300,400 today or alternatively he can pay RM60,000 in the first year, RM50,000 for the subsequent 4 years, and RM40,400 in the final year. These payments will be made at the beginning of each year. Ranjeeta is retiring in 6 years time. Because Ranjeeta does not really need the money today, she decides to let the payment(s) accumulate in a retirement account that earns 6% annual return. Which method of payment should she choose in order to get the highest value in her retirement account at the time of her retirement? Draw the timeline.

Answer 1

Option 1) : Receiving payment of RM 300,400 today

If payment is received today then Ranjeeta will invest the same in her retirement account which will fetch 6% interest every year. Amount will be invested for 6 years then interest will be paid on principal value plus interest accumulated so it can be said that interest will be compounded every year

The amount Ranjeeta will receive after 6 years;

= Amount invested * (1 + (r/n))^nt

r= rate of interest

n = number of times interest in compounded in a period

t= number of time periods

= RM 300,400 * (1+(0.06/1))^6

= RM 426,123

Option 2) Receiving payment of RM 60,000 today, RM 50,000 for subsequent 4 years and RM 40,400 in final year

Ranjeeta will invest RM 60,000 today in her retirement A/c

Interest for 1st year will be = 60,000 * 6% = RM 3,600

Ranjeeta will invest RM 50,000 in her retirement A/c in second year

Balance in A/c to calculate interest for 2nd year = 60,000+3,600+50,000 = RM 113,600

Interest for 2nd year will be = 113,600 * 6% = RM 6,816

Ranjeeta will invest RM 50,000 in her retirement A/c in third year

Balance in A/c to calculate interest for 3rd year = RM 113,600 + 6,816 + 50,000 = RM 170,416

Interest for 3rd year will be = 170,416 * 6% = RM 10,225

Ranjeeta will invest RM 50,000 in her retirement A/c in fourth year

Balance in A/c to calculate interest for 4th year = RM 170,416 +10,225 + 50,000 = RM 230,641

Interest for 4th year will be = 230,641 * 6% = RM 13,838

Ranjeeta will invest RM 50,000 in her retirement A/c in fifth year

Balance in A/c to calculate interest for 5th year = RM 230,641 +13,838 + 50,000 = RM 294,479

Interest for 5th year will be = 294,479 * 6% = RM 17,669

Ranjeeta will invest RM 40,400 in her retirement A/c in sixth year

Balance in A/c to calculate interest for 6th year = RM 294,479 +17,669 + 40,400 = RM 352,548

Interest for 6th year will be =352,548 * 6% = RM 21,153

Balance in A/c at the 6th year = RM 352,548 + 21,153 = RM 373,701

Conclusion:

In option 1 balance in A/c at the 6th year = RM 426,123

In option 2 balance in A/c at the 6th year = RM 373,701

Ranjeeta should choose option 1 as the amount is higher than the option 2. Also as she is receiving full amount in one shot so obviously it will fetch higher amount of interest to her.