Question

help plz

3) (30 pts) A Mother wanted to provide her daughter with a college education so every monthly paycheck she put $200 into the bank. If the bank was giving her 6% annual interest, how much money will the daughter have towards college after 18 years of working? a) (10 pts). Draw the cash flow diagram. Negative money is out of your pocket. b) (20 pts) What will be the future amount of money in her college account?

Answer 1

Answer:

(a) Given that the Mother deposit $200 into the bank every month for 18 years at the annual interest rate is 6%.

Thus, the effective interest rate will be i=0.5% to compound the amount monthly and maturity period will be 12*18=216 months. Therefore, i=0.5% and n=216.

i=0.5% 0 1 2 216 $200 S200 S200

(b) The future value of the total deposit of the Mother after 18 years/216 months:

We know that, future worth (FW) of equal payment series compound amount if given by

where A=equal payment=$200 and i=interest rate=0.5% and n=216

FW - *(1+i)" - 1

Thus,

FW = 4(1+i)" -1 == A(F/A, i, n) = 200 * 387.353 =77470.64

Thus the future amount of money in her college account will be $77470.64