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Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 3.5%/year compounded monthly. If the future value of the annuity after 15 years is $55,000, what was the size of each payment?

Respuesta :

Answer:

The size of each payment is $232.70.

Step-by-step explanation:

The formula to compute the future value of annuity is:

[tex]FV=P[\frac{(1+r)^{n}-1}{r} ][/tex]

Here,

FV = Future value = $55,000

r = interest rate = 3.5% = 0.035/12 = 0.00292

n = number of periods = 15 × 12 = 180

P = Periodic payments.

Compute the monthly payments as follows:

[tex]FV=P[\frac{(1+r)^{n}-1}{r} ]\\55000=P[\frac{(1+0.00292)^{180}-1}{0.00292} ]\\55000=P\times 236.3625\\P=\frac{55000}{236.3625}\\ =232.70[/tex]

Thus, the size of each payment is $232.70.