Question:
In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
Correct Answer
3
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (R) = 2% per annum
Amount (A) = $3233
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $3233 – $3050 = $183
Thus, Simple Interest = $183
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 183/3050 × 2
= 18300/6100
= 3 years (using formula)
Thus, Time (T) = 3 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $3050
Rate of Simple Interest (R) = 2% per annum
Simple Interest = $183 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 2% of Principal
= 2% of $3050
= 2/100 × 3050
= 2 × 3050/100
= 6100/100 = 61
Thus, simple Interest for 1 year = $61
Now,
∵ If the simple Interest is $61, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/61 years
∴ If the simple Interest is $183, then the time = 1/61 × 183 years
= 1 × 183/61 years
= 183/61 = 3 years
Thus, time (T) = 3 years Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(8) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.