Question

a) Suppose the interest rate is 6.6% per year compounded monthly. Compute the amount Sarah must deposit in an account today so that she can pay herself $350 per month for the next eleven years.

b) How much must Sarah deposit today if she wants to pay herself at the beginning of each month?

Please show your work :)

Answer 1

a)

Rate =6.6% / 12 = 0.55%

Number of periods = 11 * 12 = 132

Present value = Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value = 350 * [1 - 1 / (1 + 0.0055)¹³²] / 0.0055

Present value = 350 * [1 - 0.484804] / 0.0055

Present value = 350 * 93.672017

Present value = $32,785.21

You should deposit $32,785.21

b)

Rate =6.6% / 12 = 0.55%

Number of periods = 11 * 12 = 132

Present value of annuity due = (1 + r) * Annuity * [1 - 1 / (1 + r)ⁿ] / r

Present value of annuity due = (1 + 0.0055) * 350 * [1 - 1 / (1 + 0.0055)¹³²] / 0.0055

Present value of annuity due = 1.0055 * 350 * [1 - 0.484804] / 0.0055

Present value of annuity due = 1.0055 * 350 * 93.672017

Present value = $32,965.52

You should deposit $32,965.52