Question

Jayant borrowed a sum of rupees Rs. 2000 from his friend for 1year 6 months. This sum amounts to Rs. 2662 being compounded half yearly. It was found that Jayant wanted to borrow it at 10 % rate of interest. But his friend was not ready for that. When interest is compounded half yearly, then the rate should be ___________​

Answer 1

The interest rate would be 10% half-yearly or 20% yearly.

Jayant borrowed a principal amount of ₹2,000

Time period he borrowed the amount for is 1 year 6 months = 1.5 years or 3 half years.

After compounding half yearly, the total sum amounts to ₹2,662

We have to find rate. let rate be R, principal be P, total amount be A, Time period is n ( which is 3 half years ) then:

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

= 2662/2000 = ( 1 + R/100 )³

= 1331/1000 = ( 1 + R/100 )³

= (11/10) ³ = ( 1 + R/100 )³

Rate = 10% half-yearly or 20% yearly.

Answer 2

Given:

The amount jayant borrowed is 2000Rs.

he has taken money for time 1 and half year

after compound interest amount is 2662Rs.

To find: find the rate per annum.

explanation:

we have,

                Amount (A) = 2662Rs

               Principal (P) = 2000Rs.

                              n = no. of half years

                              n = 3/2 ÷ 1/2

                              n = 3

let r% be rate per half year,

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

                            $2662 = 2000(1+\frac{r}{100})^3$

                              $\frac{2662}{2000} = (1+\frac{r}{100})^3$

                                 $1.331 = (1+\frac{r}{100})^3$

                                $(1.1)^3 = (1+\frac{r}{100})^3$

as we can see exponents of both sides are the same so the base will be the same,

                                  $1.1 = 1+\frac{r}{100}$

                                  $1.1 -1 = \frac{r}{100}$

                                   $0.1 = \frac{r}{100}$

                                      r = 10% per half year

rate percent per annum will be,

                                      = 2× 10%

                                      = 20% per annum.

Hence the rate will be 10% per half year and 20% per annum.