Question

John wins $1,00,000 in a lottery and will be paid 20 equal installments of $50,000 with the first payment due today. A banker offers to exchange John’s winnings for a perpetuity of $ X per month with the first payment due today. Find the value closest to $ X assuming a 10% effective rate of interest.

(A) $3,330 (B) $3,360 (C) $3,550 (D) $3,700 (E) $3,730

I'd appreciate it if you could let me know.

Answer 1

1. Calculation of Present Value (PV) of the total receipt :

Given :

Rate of return = 10% p.a.

Period = 20

Instalemnt = $50,000

2. Calculation of monthly rate of interest :

Given:

Effective rate of ineterest = 10% p.a.

Number of Compounding in a year = 12

• Effective rate of interest = {1 + (interest for the period / number of compounding during the year)}number of compounding during the year -1

0.10 = {1 + (i/12)}12 -1

0.10 +1 = {1 + (i/12)}12

Taking 12th root on both sides :

= 1+ i/12

1.10.083333333 = 1+ i/12

1.007974140429 - 1 = i/12

On changing sides :

i/12 = 1.007974140429 - 1

i = 0.007974140429 * 12

i = 0.09568969

Therefore, monthly rate of interest = 0.09568969/12

= 0.00797414

3. Calculation of Annuity :

PV = Annuity/rate

468246.004587 = Annuity/ 0.00797414

Annuity = 468246.00457*.00797414

Annuity = $3,733.86

Conclusion : Our answer is closest to Option E that $3,730. Hence, option E is the correct answer. Some differences may be occuring because of rounding off.