Answer:
effective annual interest rate = 6.32%
annual payment = $1,585
Explanation:
I believe that this is an ordinary annuity, so we can use the future and present value of an ordinary annuity formula:
FV = annual payment x FV annuity factor, so annual payment = FV / FV annuity factor
PV = annual payment x PV annuity factor, so annual payment = PV / PV annuity factor
we can equal both equations:
PV / PV annuity factor = FV / FV annuity factor
FV / PV = FV annuity factor / PV annuity factor
$37,804.39 / $15,077.10 = FV annuity factor / PV annuity factor
2.5074 = FV annuity factor / PV annuity factor
the easiest way to solve this is to use an annuity table since we already know that there are 15 periods (I used an excel spreadsheet):
%,15 periods FV annuity factor PV annuity factor FV/PV
1 16.097 13.865 1.1609
2 17.293 12.849 1.34586
3 18.599 11.938 1.55797
4 20.024 11.118 1.80104
5 21.579 10.380 2.07890
<u>6 23.276 9.7122 2.3966</u>
<u>7 25.129 9.1079 2.7590</u>
8 27.152 8.5595 3.1721
9 29.361 8.0607 3.6425
10 31.772 7.6061 4.4112
The interest rate must be between 6 and 7%:
%,15 periods FV annuity factor PV annuity factor FV/PV
6 23.276 9.7122 2.3966
6.1 23.45404 9.6461 2.43145
6.2 23.63369 9.5858 2.46549
6.3 23.81491 9.52467 2.50034
6.31 23.83312 9.51851 2.50387
<u>6.32 23.85135 9.51236 2.5074</u>
6.4 23.99773 9.46337 2.53585
effective interest rate = 6.32% per year
annual payment = $37,804.39 / 23.85135 = $1,585
