a five - year investment has a maturity value of php 39,000. if the applied rate is 6% simple interest what…

Explanation:

Step1: Recall simple - interest formula for principal

The simple - interest formula for finding the principal $P$ when the maturity value $A$, rate $r$, and time $t$ are known is $A=P(1 + rt)$. We can re - arrange it to $P=\frac{A}{1+rt}$. Given $A = 39000$, $r=0.06$, and $t = 5$. $P=\frac{39000}{1+(0.06\times5)}$

Step2: Calculate the principal

First, calculate the denominator: $1+(0.06\times5)=1 + 0.3=1.3$. Then, $P=\frac{39000}{1.3}=30000$.

Step3: Recall simple - interest formula for total amount

The simple - interest formula for the total amount $A$ when the principal $P$, rate $r$, and time $t$ are known is $A=P(1 + rt)$. Given $P = 30000$, $r = 0.048$, and $t = 5$. $A=30000\times(1+(0.048\times5))$

Step4: Calculate the total amount for simple - interest

First, calculate the value inside the parentheses: $1+(0.048\times5)=1 + 0.24 = 1.24$. Then, $A=30000\times1.24 = 37200$.

Step5: Recall compound - interest formula for present value

The compound - interest formula for present value $PV$ is $PV=\frac{FV}{(1+\frac{r}{n})^{nt}}$, where $FV$ is the future value, $r$ is the annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the number of years. Given $FV = 200000$, $r=0.1$, $n = 12$, and $t = 5$. $PV=\frac{200000}{(1+\frac{0.1}{12})^{12\times5}}$

Step6: Calculate the present value

First, calculate the value inside the parentheses: $1+\frac{0.1}{12}\approx1.008333$. Then, $(1+\frac{0.1}{12})^{12\times5}=(1.008333)^{60}\approx1.647009$. So, $PV=\frac{200000}{1.647009}\approx121431.38$.

Answer:

The original principal is Php 30000. The total amount for a Php 30000 deposit at 4.8% simple interest for 5 years is Php 37200. The present - worth of Php 200000 to be received 5 years from now at 10% compounded monthly is approximately Php 121431.38.