In how many years will a sum of money double itself at the rate of 15 per annum simple interest

Q:

A borrows a sum of ₹2,000 from his friend B on 31 December 2011 on the condition that he will return the same after one year with simple interest at 8% per annum. However, A gets into a position of returning the money on 1 July 2012. How much amount he have to return to B?

View Answer Report Error Discuss

4 9701

Q:

A certain sum was invested on simple interest. The amount to which it had grown in five years was times the amount to which it had grown in three years. The percentage rate of interest was:

View Answer Report Error Discuss

2 875

Q:

Arvind deposited a sum of money with a bank on 1st January, 2012 at 8% simple interest per annum. He received an amount ₹ 3,144 on 7th August, 2012.

View Answer Report Error Discuss

0 869

Q:

A sum of ₹12,000 was taken at simple interest at some rate. After four months, ₹6,000 more was added and the total principal was charged at double the earlier rate of interest. At the end of the year,if the total interest was ₹2,800, what was the initial rate of interest?

View Answer Report Error Discuss

1 7714

Q:

A sum of ₹12,000 was taken at simple interest at some rate. After four months, ₹6,000 more was added and the total principal was charged at double the earlier rate of interest. At the end of the year,if the total interest was ₹2,800, what was the initial rate of

View Answer Report Error Discuss

2 6227

Q:

In how many years will a sum of yield a simple interest of at an interest rate of 10% p.a.?

View Answer Report Error Discuss

6 2232

Q:

In how many years will a sum of yield a simple interest of at an interest rate of 10% p.a.?

View Answer Report Error Discuss

1 2239

Q:

A person invested a total of ₹9,000 in three parts at 3%, 4% and 6% per annum on simple interest. At the end of a year, he received equal interest in all the three cases. The amount invested at 6% is:

View Answer Report Error Discuss

1 3526

Answer

Verified

Hint: The formula for simple interest for a principal amount P, at the rate of R % for N years is given as \[SI = \dfrac{{PNR}}{{100}}\]. Use this to equate with the given information and find the required time.Complete step-by-step answer:
The simple interest is determined by multiplying the annual interest rate by the principal amount by the number of years. If the principal amount is P, the rate is R % annually and the number of years is N, then the formula is given as follows:
\[SI = \dfrac{{PNR}}{{100}}............(1)\]
In this problem, it is given that the rate is 12 % per annum and we need to find the time in which the principal amount doubles.
Let the principal amount be P and the number of years in which the principal amount doubles be N, then the simple interest is given by the formula (1) as follows:
\[SI = \dfrac{{12PN}}{{100}}\]
Simplifying, we have:
\[SI = \dfrac{3}{{25}}PN............(2)\]
The total amount at the end of N years is the sum of simple interest and the principal amount.
\[A = P + SI\]
It is given that this amount is two times the principal amount, hence, we have:
\[2P = P + SI\]
Solving for the simple interest, we have:
\[SI = 2P - P\]
\[SI = P...........(3)\]
Equating equation (2) and equation (3), we have:
\[P = \dfrac{3}{{25}}PN\]
Canceling P on both sides, we have:
\[1 = \dfrac{3}{{25}}N\]
Solving for N, we have:
\[N = \dfrac{{25}}{3}years\]
$N$ = $8years$ $4months$
Hence, the required time is 8 years and 4 months.

Note: You might make a mistake by substituting the simple interest as equal to twice the principal amount. The amount, which is the sum of principal and simple interest is equal to twice the principal. Hence, the simple interest for the period will be equal to the principal amount.

In what time will a sum of money double itself at 15% P?

How many years will a sum of money double itself?

In what time will a sum of money put at 15% simple interest triple itself?

How many years will a sum of money double itself at the rate of 5% per annum?