Question:
Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11020
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 = $11020 – $5800 = $5220
Thus, Simple Interest = $5220
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 × 5220/5800 × 9
= 522000/52200
= 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) = $5800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $5220 (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 = 9% of Principal
= 9% of $5800
= 9/100 × 5800
= 9 × 5800/100
= 52200/100 = 522
Thus, simple Interest for 1 year = $522
Now,
∵ If the simple Interest is $522, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/522 years
∴ If the simple Interest is $5220, then the time = 1/522 × 5220 years
= 1 × 5220/522 years
= 5220/522 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(3) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(7) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?
(8) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.