Question is below V (Math) (Finance)

Question

Hannibal opens a savings account on January 1, 1984 with a deposit of 330 dollars, and continues to make deposits of the same amount at the beginning of each month until January 1, 1990, when he makes the final deposit. If the account pays a nominal rate of interest of 4.7 percent convertible monthly, how much is in the account on January 1, 1998?

Answer 1

First calculate the PV of the deposit stream. Thia would be the same as the present value of a stream of loan payments discounted at a 4.7% rate.

PV= PMT*(1/i)(1-(1/(1+i)^T)) i = 4.7%/12 T= 6 years plus 1 month ( all of 1984 though 1989 and the first month of 1990) = 73 months.

Let the PV multiplier, k = (1/i)(1-(1/(1+i)^T)) = (12/4.7%)*(1 - (1/(1+.047/12))⁷³)

k= 15.735 so PV = 330k = 5192.70

Now we want to know what 5192.70 will be worth 14 years later (168 months) sooo

FV = PV(1+i)^T i=4.7%/12 so we get FV =5192.70*(1+.047/12)¹⁶⁸= 10,013.52

I am more than happy tyo help you out here.