Find the monthly payment require to save 50000 in 10 years i

Find the monthly payment require to save $50,000 in 10 years if our payments earn 6% annual interest compounded monthly.

Solution

The formula for future value (F) of an ordinary annuity is F = p [{(1 + r)ⁿ – 1} / r], where p is the amount of each annuity payment, r is the interest rate per term/period in decimals and n is the number of terms/periods over which payments are made. Here, F = $50000, r = 0.06/12 = 0.005 and n = 10*12 = 120. Then, we have 50000= p [ { (1 + 0.005)¹²⁰ -1}/ 0.005} or, 50000= p[ {(1.005)¹²⁰ -1}/ 0.005 ] = p(1.819396734 -1)/ 0.005 = p*0. 819396734/ 0.005 = 163.8793468p. Therefore, p = 50000/163.8793468 = $305.10 (approximately, on rounding off to the nearest cent). Thus, the required monthly payment is $ 305.10.