The Moores are close to retirement. They agree to sell an antique urn to a local museum for
$17,000. Their tax adviser suggests that they defer receipt of this money until they retire, 5
years in the future. The museum agrees to pay them the $17,000 in a lump sum in 5 years.
Assume that the museum can earn 8% compounded annually on its money and that the
payment are made annually.
(a) Find the amount of each payment the museum must make into a sinking fund so that it
will have the necessary $17,000 in 5 years.
What i did=
n=5, i=0.08, S=17000
17000(0.08)/(1.08)^5-1= $2897.76
Is the answer correct? I feel like its not that easy and just go with the formula or am i having the wrong formula../
You are correct.
It is that easy, since this is a very standard question.
You used the formula
Future Amount = Paym( (1+i)^n - 1)/i
Your approach is correct, but you need to adjust your formula slightly. The formula you're using is for finding the periodic payment needed to accumulate a certain future value, but in this case, you're trying to find the periodic payment needed to accumulate $17,000 in 5 years.
Here's the correct formula to use in this scenario:
P = S / ((1 + i)^n - 1)
Where:
P = periodic payment
S = desired future value (in this case, $17,000)
i = interest rate per period (in this case, 8% or 0.08)
n = number of periods (in this case, 5 years)
Plugging in the values:
P = 17000 / ((1 + 0.08)^5 - 1)
P = 17000 / (1.08^5 - 1)
P = 17000 / (1.46933 - 1)
P = 17000 / 0.46933
P ≈ $36,215.56
So, the amount of each payment the museum must make into a sinking fund is approximately $36,215.56.
Your approach is almost correct, but you made a small mistake in the formula you used to calculate the amount of each payment.
The correct formula to use in this case is the sinking fund formula, which is given by:
P = (S * i) / (1 - (1 + i)^(-n))
where:
P = Amount of each payment
S = Future value or desired amount ($17,000 in this case)
i = Interest rate per period (8% or 0.08 as a decimal)
n = Number of periods (5 years in this case)
Now let's plug in the values and calculate the amount of each payment:
P = (17000 * 0.08) / (1 - (1 + 0.08)^(-5))
P = 1360 / (1 - 1.46933)
Calculating the denominator:
1 - 1.46933 = -0.46933
Now dividing:
P = 1360 / -0.46933
P ≈ -2898.48
The amount of each payment should be approximately -$2898.48. The negative sign indicates that this is an outgoing payment from the museum, representing their contribution to the sinking fund.
Note: The negative sign in the result arises because the formula assumes that cash inflows (payments from the museum) are positive, while cash outflows (payments to the sinking fund) are negative.