Question

Shikha borrowed a loan of 1,80,000 for constructing
a room from a bank for 5/2 years, compounded
annually at 45/4 % per annum. How much amount will
she return after 5/2 years?​

Answer 1

Answer:

After 5/2 years she will return an amount of 2,34,975.

Step-by-step explanation:

• Compound interest: The formula for compound interest is:

                                            C.I = $P(1 + \frac{r}{100} )^t$ - P

   Here C. I = compound interest, P = principal amount, r = rate of interest,      t = time taken.

The total amount after t time = A = P + C.I. = P +  $P(1 + \frac{r}{100} )^t$ - P

                                                                        = $P(1 + \frac{r}{100} )^t$

• Given data: Principal amount = P = 1,80,000

       t = $\frac{5}{2}$ years,  r = $\frac{45}{4}$.   Here we have to find the total amount.

• Total amount:  A = $P(1 + \frac{r}{100} )^t$ = $180000(1 + \frac{45}{4\times 100} )^\frac{5}{2}$

                                                            = 180000 × $\sqrt{(1 + 0.1125)^{5}}$

                                                            = 180000 × $\sqrt{(1.1125)^{5}}$

                                                            = 180000 × 1.1125 × 1.1125 × $\sqrt{(1.1125)}$

                                                            = 2,34,975

   ∴ After 5/2 years she will return an amount of 2,34,975.

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Answer 2

The amount that she will return after 5/2 years is Rs. 2,34,936.

Given: Shikha borrowed a loan of 1,80,000 for constructing a room from a bank for 5/2 years, compounded annually at 45/4 % per annum.

To Find: The amount that she will return after 5/2 years.

Solution:

We can find the amount received after a certain period when a loan is compounded annually, which can be given by the formula,

                  A = P × ( 1 + ( R/100 ))^n                                          .......(1)

Where A = Amount to be returned, P = Principle amount taken, R = rate of interest, n = time for which principle amount is taken.

Coming to the numerical, we are given;

The principle amount (P) = Rs. 180000

The rate of interest (R) = 45/4 % per annum

The time taken (n) = 5/2 years

Putting the respective values in (1), we get;

              A = P × ( 1 + ( R/100 ))^n  

          ⇒ A = 180000 × ( 1 + ( 45 / 400 ))^(5/2)

          ⇒ A = 180000 × ( 445 / 400 )^(5/2)

          ⇒ A = 180000 × ( 89 / 80 )^(5/2)

          ⇒ A = 180000 × 1.3052

          ⇒ A = 2,34,936

Hence, the amount that she will return after 5/2 years is Rs. 2,34,936.

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