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

Initial principal -$300,000

Investment amount after yr 3-$390,000

Final investment amount, after 6 yrs-$519,090

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* 0.1* 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*1.1\\\\=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* 0.1* 3\\\\A=1.3X\\\\=1.3* 300000\\\\=390000`

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