Question

When the interest rate is a constant 10% p.a., an annuity with 25 constant annual payments has a future value of $49,173.53 at the last payment. What is the constant annual payment amount?

		$450.38
		$500.00
		$1,000.00
		$1,966.94
		Cannot be determined, insufficient information

Answer 1

Option (b) is correct

Here, the deposits will be same every year, so it is an annuity. The future value of annuity is $49173.53. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity = $49173.53, P is the periodical amount, r is the rate of interest = 10% and n is the time period = 25

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

$49173.53 = P * ((1 + 10%)²⁵ - 1 / 10%)

$49173.53 = P * ((1 + 0.10)²⁵ - 1 / 0.10)

$49173.53 = P * ((1.10)²⁵ - 1 / 0.10)

$49173.53 = P * ((10.8347059434- 1 / 0.10)

$49173.53 = P * (9.8347059434/ 0.10)

$49173.53 = P * 98.3470594339

P = $49173.53 / 98.3470594339

P = $500

So, constant payment amount is $500.