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2. Xandrea borrowed some money from a bank that offers an interest rate of 12%
compounded monthly. His monthly amortization for 5 years is P11,122.22. How
much is the outstanding balance after the 12th payment?
​

Sagot :

Answer:

[tex]\huge \red{\overline{ \qquad \qquad \qquad \qquad \qquad}}[/tex]

Xandrea borrowed some money from a bank that offers an interest rate of 12% compounded monthly. His monthly amortization for 5 years is P11,122.22. How much is the outstanding balance after the 12th payment?

[tex] \sf{ \underline{Solution:}}[/tex]

[tex] \sf{Given:}[/tex]

[tex]P = 11,122.22\: \\ {i}^{12} = 0.12 \\ j = \frac{ {j}^{12} }{12} = \frac{0.12}{12} = 0.01 \\ k = 12 \\ n - k = 48 { \sf{ \: since \: only}} \: \green{ \underline \red{48}}{ \sf{ \: payments \: remain \: }}[/tex]

[tex] \sf{Find:}[/tex]

Present value of 48 future payments ( since there are 48 payments left )

[tex]k = R[ \frac{1 - (1 + j)^{n - k} }{j} ] = 11,122.22 \\ [ \frac{1 - (1.01) ^{ - 48} }{ 0.01} ] = 422,354.73 [/tex]

The outstanding balance is [tex] \sf{ \underline{422,354.73}}[/tex]

[tex]\huge \red{\overline{ \qquad \qquad \qquad \qquad \qquad}}[/tex]

Step-by-step explanation:

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