Question

How much should Miguel's dad invest into a savings account today, to be able to pay for Miguel's rent for the next 6 years if rent is $600 payable at the beginning of each month? The savings account earns 3.5% compounded monthly.

Answer 1

This the problem of present vlaue of annuity due

Present value of annuity due = P + P * (1 - (1 + r)^-(n-1))/r

P is periodic payment which is $600

r is interest rate = 3.5%/12 = .29167%

n = 12*6

Present value of annuity due = 600 + 600 * (1 - (1 + .0029167)^-(71))/.0029167

= 600 + 38428.01

= $39028.01

Thus Migule's father need to deposit $39028.01 in saving account.