Question

Yi wants to open his own bakery in 6 years. To do so, he needs to accumulate $200,000 (in today's dollars) at that time. He assumes he can ear a 9% compound annual after-tax rate of return on investment and inflation will average 4%. What will Matt's serial payment be at the end of the second year?

A) $30,491.00

B) $30,727.95

C) 28,190.78

D) 31,957.07

Answer 1

After adjusting the target amount of $200,000 for 4% inflation over 6 years and using the annuity due formula with a 9% interest rate, Yi's serial payment at the end of the second year is approximately $30,727.95, which is option B.

Step-by-step explanation:

The correct option : c

To calculate the serial payment Yi needs to make at the end of the second year, we first need to adjust the target amount for inflation, as the $200,000 is in today's dollars. We use the future value formula that includes inflation. The adjusted future value (FV) Yi needs in 6 years is calculated as:

FV = Present Value * (1 + inflation rate)number of years

So for a $200,000 goal with a 4% inflation over 6 years, the calculation is:

FV = $200,000 * (1 + 0.04)6

Once we have the future value considering inflation, we need to compute the annual payment Yi needs to make. We calculate Yi's serial payment using the present value of an annuity due formula:

PMT = FV / [(1 + i)n - 1 / i]

where PMT is the payment, i is the interest rate (9% adjusted for annual compounding), and n is the number of years left (4 years). This gives us the payment required at the end of the second year to reach the adjusted future value in 6 years.