Question

A sum of money is placed at simple interest for 3 years at 10% annum and then the amount is invested for 3 years at the same rate at compound interest. if the total amount of 5 years became Rs,471900. what was the sum.​

Answer 1

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:

$I=PRT\\\\A=P+I\\\\A=X+X\times 0.1\times 3\\\\A=1.3X$

#The amount after 5 yrs is calculated by compounding the amount after 3 yrs for 2 yrs at 10%:

$A=P(1+i)^2\\\\471900=1.3X(1.1)^2\\\\471900=1.573X\\\\X=300000$

Hence, the amount initially invested as $300,000

#Amount of invested after 6 yrs is therefore:

$A=P(1+i)^n\\\\=471900\times1.1\\\\=519090$

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:

$I=PRT\\\\A=P+I\\\\A=X+X\times 0.1\times 3\\\\A=1.3X\\\\=1.3\times 300000\\\\=390000$

Hence, the total amount of the investment after first 3 yrs is $390,000