Question

What is the future value of a $400 per year ordinary annuity for ten years at 10 percent? Note: provide answer in full dollars/cents form, e.g., $1,234.56

Answer 1

An ordinary annuity has payments made at the end of each period, while an annuity due has payments made at the beginning of each period.

Now, let's calculate the future value of the annuity due, given that the future value of the ordinary annuity is $100,000 and the interest rate is 5 per cent.

Step 1: Determine the future value factor of the ordinary annuity.

Future Value of Ordinary Annuity (FVOA) = $100,000

Interest Rate (r) = 5% = 0.05

Number of Periods (n) = 5 years

Step 2: Use the FVOA formula to find the annuity payment (PMT).

FVOA = PMT * [(1 + r)ⁿ - 1] / r

$100,000 = PMT * [(1 + 0.05)⁵ - 1] / 0.05

PMT = $18,039.37 (approx.)

Step 3: Calculate the future value of the annuity due (FVAD).

FVAD = PMT * [(1 + r)ⁿ - 1] / r * (1 + r)

FVAD = $18,039.37 * [(1 + 0.05)⁵ - 1] / 0.05 * (1 + 0.05)

FVAD = $105,000 (approx.)

Explanation: