Question

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is

Answer 1

A₁ = ₹9800   T₁ = 5 yrs
A₂ = ₹12005  T₂ = 8 yrs
Therefore, SI for 3 yrs = 12005 - 9800 = ₹2205
Therefore, SI for 1 yr = $\frac{2205}{3}$ = ₹735
SI₁ (for 5 yrs)= 735 × 5 = ₹3675
P = A₁ - SI₁ = 9800 - 3675 = ₹6125
Therefore, R p.a. = 100 × SI₁ / P × T₁ = 100 × 3675 / 6125 × 5 = 12%

Answer 2

Given:

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest.

To Find:

The rate of interest per annum is

Solution:

We need to the formula for simple interest that is

                                 $I=\frac{PRT}{100}$

where,

          P= principal amount

          R= rate of interest

          T= time period

Now the amount after a specific time period will be

$A=P+\frac{PRT}{100}$

Now using the given situation that Rs 9800 is obtained after 5 years for which we can formulate an equation

$9800=P+\frac{5PR}{100}$     -(1)

Now for the other situation, Rs 12005 is obtained after 8years for which we can formulate an equation as

$12005=P+\frac{8PR}{100}$   -(2)

Now subtracting equation 2 with equation 1 we get

$\frac{3PR}{100} =2205\\PR=73500$

Now putting this value in equation 1 to find the value principal sum

$P+\frac{73500*5}{100}=9800\\P=6125$

So using PR=73500 we find the rate of interest as

$R=\frac{73500}{6125} \\=12$

Hence, the rate of interest is 12%.