Question

Mr. Gupta has been accumulating a fund at $8\%$ effective, which will provide him with an annual income of Rs $30000$ for $15$ years, the first payment being paid on his ${60}^{th}$ birthday. If he wishes to reduce the number of payments to $10$, find how much annual income (in Rs) will he receive?

• A. $38268$
• B. $30268$
• C. $38208$
• D. $38068$

Answer 1

The correct option is A $38268$

In first case, we have annuity due of $15$ terms.
Its present value (as on Mr. Gupta's ${60}^{th}$ birthday),
$v=\frac{A}{r}\times (1+r)\times [1-(1+r{)}^{-n}]$
= $\frac{3000}{0.08}\times 1.08\times [1-(1.08{)}^{-15}]$
Now if only $10$ payments are to be received, we have annuity due of $10$ terms. If A is the amount of each annual installment,
$\frac{A}{0.08}\times 1.08\times [1-(1.08{)}^{-10}]$
Thus,
$\frac{A}{0.08}\times 1.08\times [1-(1.08{)}^{-10}]$ = $\frac{3000}{0.08}\times 1.08\times [1-(1.08{)}^{-15}]$
A = $30000\times \frac{[1-(1.08{)}^{-15}]}{[1-(1.08{)}^{-10}]}$
A = $38268$