Question

Sabina is a married woman in her late thirties. She wants to assure that should she die prematurely her family would be assured of her income for life. She is currently making $6,850 per month and believes that the return on investment should be 2.5%. Given this scenario, how much capital is required to satisfy this goal?

A. $3,420,000
B. $2,052,000
C. $1,377,000
D. $820,000

Answer 1

To determine the capital required for Sabina to assure her family's income at a 2.5% return rate, a present value calculation is used. The closest correct option to the calculated capital of $3,288,000 is A. $3,420,000.

Step-by-step explanation:

The student is asking about how much capital Sabina would need to ensure that her income is replaced for her family in the event of her death, assuming a return on investment of 2.5%. To calculate this, we need to determine how much capital would need to be invested to generate $6,850 per month (her current income) at a 2.5% annual rate of return. This is a present value calculation of an annuity done by using the following formula:

PV = PMT / i

Where PV is the present value (the capital needed), PMT is the monthly payment (Sabina's monthly income), and i is the monthly interest rate (annual rate / 12).

First, we convert the annual interest rate to a monthly rate:

0.025 / 12 = 0.002083333

Next, we can plug in Sabina's monthly income for PMT:

PV = $6,850 / 0.002083333

PV = $3,288,000

Therefore, the amount of capital required for Sabina's goal is $3,288,000, which doesn't exactly match any of the options provided in the question. So the closest correct option would be A. $3,420,000.