Question

Smriti invested Rs 20,000 in the bank for 4 years and got back rs 29,282 after 4 years . What was the rate of interest per annum payable annually ? Answer should be 10% . ​

Answer 1

Answer:

10%

Step-by-step explanation:

We are given that Sangeeta invested RS. 20000/- in the bank.

Let us assume that the principal amount that Sangeeta invested as

⇒P=20000

We are given that she gets total of RS. 29282/-

Let us assume that the amount she gets finally as

⇒A=29282

We are given that the time period as 4 years.

Let us assume that the time period as

⇒T=4

Now, let us assume that the rate of interest per annum as ′R′

We know that the formula for amount in the compound interest is given as

⇒A=P(1+R100)T

Where, ′A′

Now, by using the above formula to given data we get

⇒29282=20000(1+R100)4⇒(1+R100)4=2928220000

Now let us divide the numerator with 2 in the RHS then we get

⇒(1+R100)4=1464110000

Here, we can see that there is a power of 4 on LHS.

So, let us convert the RHS also as a power of 4 because we have 114=14641

and 104=10000

then we get

⇒(1+R100)4=(1110)4

We know that if an=bn

then a=b

Now, by using this theorem to above equation we get

⇒(1+R100)=1110⇒R100=1110−1⇒R=10%

Therefore, the rate of interest per annum is 10%.