Question

might capital is 5/4 times more than tulsis capital . Tulsi invested her capital at 50% per annum for 3 (compounded annually ) at what rate % p.a. simple interest should mihir invested his capital so that after 3 years , they both have the same amount of capital ?​

Answer 1

Answer:

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Answer 2

Answer:

Concept:

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common. In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time. The simple yearly interest rate is obtained by multiplying the interest per period by the total number of periods in a year.

Given:

Might capital exceeds tulsis capital by a factor of 5/4. What percentage p.a. simple interest rate should Mihir invest his cash at so that after three years, they both have the same amount of capital? Tulsi invested her capital at 50% per year for three (compounded annually).

Find:

find the solution for the given question

Answer:

The capital of Tulsa should be $x$

The capital of Mihir is $\frac{5}{4}$ times that of Tulsi.

Then Mihir's Capital $=x+\frac{5x}{4}$

                                  $=\frac{9x}{4}$

Tulsi put her money into investments for three years at $50$% annually (compounded annually).

Total amount of Tulsi $=P(\frac{1+r}{100} )^{3}$

                                    $=x(\frac{1+50}{100} )^{3}$

                                     $=x(\frac{3}{2} )^{3}$

                                     $=x*\frac{27}{8} ----- > (1)$

The complete quantity of Tulsi $=x*\frac{27}{8}$

Mihir put his money into simple interest investments, so

The total sum is Mihir $=P+SI$

                                    $=(\frac{9x}{4} )+(\frac{9x}{4} )*R*\frac{3}{100} ------(2)$

$x*\frac{27}{8} =(\frac{9x}{4} )+(\frac{9x}{4} )*R*\frac{3}{100}$

$x*\frac{27}{8} =\frac{9x}{4} (1+\frac{3R}{100} )$

$\frac{3}{2} =1+\frac{3R}{100}$

$\frac{3}{2} =\frac{(100+3R)}{100}$

$300=200+6R$

$6R=100$

$R=\frac{100}{6}$

   $=\frac{50}{3}$%

Hence the Rate is $=50/3$%.

The initial principal sum is increased by both of these variables, and the annual interest rate is increased to the number of compounded periods minus one. The resulting value is subsequently deducted from the loan's entire original amount.

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