Question:
Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8840
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 = $8840 – $5200 = $3640
Thus, Simple Interest = $3640
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 × 3640/5200 × 7
= 364000/36400
= 10 years (using formula)
Thus, Time (T) = 10 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) = $5200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $3640 (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 = 7% of Principal
= 7% of $5200
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = 364
Thus, simple Interest for 1 year = $364
Now,
∵ If the simple Interest is $364, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/364 years
∴ If the simple Interest is $3640, then the time = 1/364 × 3640 years
= 1 × 3640/364 years
= 3640/364 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
(4) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.