Answer:
Initial principal -$300,000
Investment amount after yr 3-$390,000
Final investment amount, after 6 yrs-$519,090
Step-by-step explanation:
Let X be the amount initially invested.
#The amount after 3 yrs of simple interest is calculated as:
[tex]I=PRT\\\\A=P+I\\\\A=X+X\times 0.1\times 3\\\\A=1.3X[/tex]
#The amount after 5 yrs is calculated by compounding the amount after 3 yrs for 2 yrs at 10%:
[tex]A=P(1+i)^2\\\\471900=1.3X(1.1)^2\\\\471900=1.573X\\\\X=300000[/tex]
Hence, the amount initially invested as $300,000
#Amount of invested after 6 yrs is therefore:
[tex]A=P(1+i)^n\\\\=471900\times1.1\\\\=519090[/tex]
Hence, the total amount of the investment after 6 yrs is $519,090
#Substitute X in simple interest equation to find amount after 3 yrs of simple interest:
[tex]I=PRT\\\\A=P+I\\\\A=X+X\times 0.1\times 3\\\\A=1.3X\\\\=1.3\times 300000\\\\=390000[/tex]
Hence, the total amount of the investment after first 3 yrs is $390,000
