Question 1195215
In return for a loan, with money worth 7% compounded semiannually, a man promises to pay $600 at the end of each 6 months for 8 years. (b) Find his remaining liability just after his 6th payment.
<pre>One needs to calculate the Present Value (PV<sub>oa</sub>) of an annuity with a semi-annual (2) payment of $600, an annual interest rate of 7% (.07),
and a remaining term of 5 years (8 years - 3 years, or 6 semi-annual payments).
    So, we have: {{{system(matrix(1,3, PV[oa], "=", PMT((1 - 1/(1 + i/m)^(mt))/(i/m))), or, matrix(1,3, PV[oa], "=", PMT(1-1/(1+i/m)^(mt))(m/i)))}}}

Using the latter, we get: {{{matrix(1,3, PV[oa], "=", 600(1 - 1/(1 + .07/2)^(2(5)))(2/.07))}}}
Remaining balance after 6 semi-annual payments/3 years, or 
                          {{{highlight_green(matrix(1,11, PV[oa], "=", 600(1 - 1/1.035^10)(2/.07), "=", 4989.963194, "=", highlight("$4,989.96"), "(rounded", to, nearest, "cent)")))}}}</pre>