An education fund of $40,000 is to be accumulated by making payments of $400 at the end of every 3-month period,plus a smaller concluding payment.Determine the number of full payments required if j₄ = 9%. A)50 B)51 C)52 D)53

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity to solve this problem:

PV = (PMT/i) * (1 - (1/(1+i)^n))

where PV is the present value (in this case, $40,000), PMT is the payment ($400), i is the interest rate per period (9%/4 = 2.25%), and n is the number of periods.

Substituting in the known values, we get:

$40,000 = ($400/0.0225) * (1 - (1/(1.0225)^n))

$40,000 = $17,777.78 * (1 - (1/1.0225)^n)

2.25 = (1/1.0225)^n

log(2.25) = n*log(1.0225)

n = log(2.25)/log(1.0225)

n = 52.65

Since we can't have a fraction of a payment, we round up to the nearest whole number, which gives us 53. However, we need to subtract the smaller concluding payment, so the actual number of full payments required is 52. Therefore, the answer is (C).

An Education Fund of $40,000 Is to Be Accumulated by Making