Question

5. (4 marks) You have just read an ad which says: "Deposit $550,000 with us today and we will pay you $50,000 a year from now and SX per year from year I to year 25. If this is a fair deal, and the interest rate is 4%, how much is ? Use 3 decimal points in your calculations.

Answer 1

Deposit Amount = $550,000

Current Payment = $50,000

Payment From Year 1 to 25 = $X

Interest rate (i) = 4%

No. of payment from year 1 to 25 (n) = 25

Thus,

Present value of Annual payment of $X (P) = 550000-50000= $500,000

We can compute the value of X with following equation

$X = P*\left (\frac{ i(1+i)^n}{(1+i)^n-1} \right )$

putting the values,

$X = 500,000*\left (\frac{ 0.04(1+0.04)^{25}}{(1+0.04)^{25}-1} \right )$

$\large X = \$32,000$

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.