Tony saved enough money to place $125,500 in an investment generating 10% compounded monthly. He wants to collect a monthly income of $1,350, at the beginning of each month, for as long as the money lasts. How many months will Tony have this income coming to him?

A. 165.

B. 145.

C. 192.

D. 162.

The answer is 162 months, option (D)

Explanation:

Solution

Given that:

Tony saved an amount of money = $125,500

Investment generates a = 10% compounded monthly

A monthly income of = $1350

Now, we have to find How many months will Tony have this income coming to him

Thus

The current income value will be equal to = $125,500.

So,

125,500 = 1350 + 1350/1.0077 + 1350/1.0077^2 + 1350/1.0077^3 + ... + 1350/1.0077^n

125,500 = 1350 * 1.0077 / 0.0077 * (1 - (1/1.0077) ^n)

Therefore n = 162 months