Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 4.5%/year compounded monthly. If the future value of the annuity after 14 years is $50,000, what was the size of each payment? (Round your answer to the nearest cent.)

each payment = $214.20

Step-by-step explanation:

For ordinary annuity,

FVOA = PMT x [{ (1+r/m) ^ (n*m) } - 1 / (r/m) ]

Here, FVOA = $50,000

year, n = 14

Since the interest will be paid monthly, m = 12

interest rate, r = 4.5% = 0.045

PMT = ?

Putting all the values into the ordinary annuity formula,

FVOA = PMT x [{ (1+r/m) ^ (n*m) } - 1 / (r/m) ]

$50,000 = PMT x [{ (1+0.045/12) ^ (14*12) } - 1 / (0.045/12) ]

or, $50,000 = PMT x [{ (1+0.045/12) ^ (14*12) } - 1 / (0.045/12) ]

or, $50,000 = PMT x [ (1.8754 - 1) / 0.00375]

or, $50,000 = PMT x [ (1.8754 - 1) / 0.00375]

or, $50,000 = PMT x 233.4399

or, PMT = $50,000/233.4399

PMT = $214.19

or, monthly payment will be $214.20 (Nearest cent)