Ordinary simple annuity, N

[Crunchie]

I have a question regarding Ordinary simple annuity. seems like im overlooking something and missing a step in converting. The answer key tells me 7 years, 10 months. I come up with .93078580 which i then divide by 12 since its 12 payments in a year or a final of 7.8 years rounded.

Find the term of the following ordinary annuity, state in years and months.

Present value: 14,500
Periodic Rent: 190
Payment interval: 1 month
Interest rate: 5.25
Conversion Period: Monthly

I come up with the following:

Step 1:
n= -in [ 1- ( 14,500 ) .004375 ]
190
___________________
in (1+.004375)

Step 2:
-in [ 1- (76.315789) (.004375)
------------------------------
in (1.004375)

Step 3:
-in [1- (.333882)]
-------------------
in (1.004375)

Step 4:
-in (.666118)
---------------
in (1.004375)

Step 5:
(.406288)
---------
.004365

n= 93.078580/12= 7.756548, rounded to 7.8 years.

 

[Crunchie]

Another one?

I have another one as well, The answer key says N= 15.577564 half years, with a final answer of 8 years, how does this convert into 8 years?