Question

Candy Company sells an asset with a$3,000,000 fair value to Emily,Inc.Emily agrees to make 6 equal payments,each to be paid one year apart,starting on the date of sale.The payments include

principal and 3%annual interest.What is the required annual installment payment?

Answer 1

Here, the payments will be same every year, so it is an annuity. And the payments start at the beginning of each year, so it is an annuity due. We will use the future value of annuity due formula tpo calculate the annual payments as per below:

FVAD = (1 + r) * P * ((1 + r)ⁿ - 1 / r)

where, FVAD is future value of annuity due = $3000000, P is the periodical amount, r is the rate of interest = 3% and n is the time period = 6

Now, putting these values in the above formula, we get,

$3000000 = (1 + 3%) * P * ((1 + 3%)⁶ - 1 / 3%)

$3000000 = (1 + 0.03) * P * ((1 + 0.03)⁶ - 1 / 0.03)

$3000000 = (1.03) * P * ((1.03)⁶ - 1 / 0.03)

$3000000 = (1.03) * P * ((1.19405229653- 1) / 0.03)

$3000000 = (1.03) * P * (0.19405229653 / 0.03)

$3000000 = (1.03) * P * 6.4684098843

$3000000 = P * 6.66246218

P = $3000000 / 6.66246218

P = $450283.98

So, annual instalment payment is $450283.98