Answer:
the first part of the question is missing:
Suppose that you make a sequence of 31 equal monthly deposits into an account paying a nominal rate of 6.7% convertible quarterly.
we need to determine the present value of the $8,000 at the moment that you stop making the monthly payments.
the effective annual interest rate = (1 + 6.7%/4)⁴ - 1 = 6.87%
the effective monthly interest rate = (1 + 6.87%)¹/¹² - 1 = 0.55523%
the value at the moment that you finish making the deposits = $8,000 / (1 + 0.0055523)⁷ = $7,695.86
now we can calculate the monthly payments using the future value of an annuity formula:
future value = monthly payment x FV annuity factor
monthly payment = future value / FV annuity factor
- future value = $7,695.86
- FV annuity factor, 31 periods, 0.55523% = 33.72594
monthly payment = $7,695.86 / 33.72594 = $228.19