To finance the purchase of a car, Wendy agrees to pay $\$400$ at the end of each month for 4 years. The interest rate is j12 = 15%.
Assuming Wendy has missed no payments, what single payment at the end of 2 years would completely discharge her of her indebtedness?
$R = \$400$
$i = 0.15/12 = 0.0125$
$n = (4 \cdot 12)-(2 \cdot 12) = 24$
I've used the Discounted Value formula: $R\cdot [1-(1 + i)^{-n}]/i$
$400 \cdot [1-(1.0125)^{-24}]/0.0125 = 8249.693805$
But, this is not the right answer. Please help me figure out the right answer.
I would first calculate the future value at $t=24$ (months) of the first $23$ payements. This is
$$400\cdot \frac{1.0125^{23}-1}{0.0125}\cdot 1.0125=10,715.23$$
Then calculating the value at $t=24$ (months) of the $48$ payments.
$$\underbrace{400\cdot \frac{1.0125^{48}-1}{0.0125}}_{\texttt{Value of 48 payments at t=48}}\cdot \underbrace{\frac1{1.0125^{24}}}_{\texttt{Dicounting 24 months}}=19,364.93$$
The difference is the final payment which Wendy has to make.