You're prepared to make monthly payments of $220, beginning at the end of this month, into an account that pays 6.3 percent interest compounded monthly. How many payments will you have made when your account balance reaches $13,000?

52 payments

Explanation:

A constant payment for a specified period is called annuity. The future value of the annuity can be calculated using a required rate of return.

Formula for Future value of annuity is

FV = P x ([ 1 + i ]^n - 1) / i

P = Payment amount = $220

i = interest rate = 6.3% / 12 = 0.525%

FV = Future value = $13,000

n = Number of payments

$13,000 = 220 x ([ 1 + 0.525% ]^n - 1) / 0.525%

($13000 x 0.525%) / $220 = [ 1 + 0.525% ]^n - 1

0.31 = [ 1 + 0.525% ]^n - 1

0.31 + 1 = [ 1.00525 ]^n

1.31 = 1.00525^n

Log 1.31 = n log 1.00525

n = Log 1.31 / log 1.00525

n = 51.6 payments = 52 payments (rounded off to nearest whole number)