Question

Find the payment necessary to amortize the loan.$10,000; 8% compounded annually; 10 annual paymentsO $1490.29O $1600.79O $1400.76O $1490.07nuoction 24

Answer 1

Answer:

The annual payment = $1490.29

Step-by-step explanation:

The loan is the Present Value (PV)

PV = $10000

The annual rate, r = 8%

r = 8/100

r = 0.08

The number of payments, n = 10

The Present Value of annunity is given by the formula:

`PV\text{ = P\lbrack}(1-(1+r)^(-n))/(r)\rbrack`

Substitute PV = 10000, r = 0.08, and n = 10 into the formula above to solve for P

`\begin{gathered} 10000=P\lbrack(1-(1+0.08)^(-10))/(0.08)\rbrack \\ 10000*0.08=P\lbrack1-(1.08)^(-10)\rbrack \\ 800\text{ = P(1-}0.4632) \\ 800\text{ = }0.5368P \\ P\text{ = }(800)/(0.5368) \\ P\text{ = }1490.29 \end{gathered}`

The annual payment = $1490.29