annual payments of P12,500 with an interest rate of 10.5% compounded semi-annually for 6 years. Simple or General annuity? and why?. Created by Dakzy69. Math

annual payments of P12,500 with an interest rate of 10.5% compounded semi-annual...

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$\large\color{skyblue}{\underline{\underbrace{\bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \:\: \: \: \: \: \: \:Answer : \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \:}}}}$

Annual payments of P12,500 with an interest rate of 10.5% compounded semi-annually for 6 years?

$\implies$ $\large\red{₱35,598.04}$

Simple or General annuity? and why?

$\implies$ The main difference is that in a simple annuity the payment interval is the same as the interest period while in a general annuity the payment interval is not the same as the interest period.

$\small\blue{-Discoloration$

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Discoloration

Annual payment of P12,500 with an interest rate of 10.5% compounded semi-annually for 6 years?

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ANSWER: P35,596.00

GENERAL ANNUITY, is an annuity where the payments do not coincide with the interest period ( . )

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Solution:

$\: \small\tt{p =₱12,500.00 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \small\tt{r = 10.5\% \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \small\tt{t = 6 \: years \: compounded \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \small\tt{semi - annually \: \: \: \: \: \: \: \: \: \: } \\ \small\tt{compound = p(1 + \frac{r}{200} )2t \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \small\tt{2interest \: \: \: \: \: \: } \\ \small\tt{ = 12,500(1 + \frac{10.5}{200} )2 \times 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \small\tt{ =₱23,098.04 } \\ \\ \small\tt{amount \: f = p + ci \: = ₱35,596.04 \: \: \: \: } \\ \small\tt{the \: answer \: is \: \color{green}{₱35,598.04}}$

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