Question:
Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9086
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 = $9086 – $5900 = $3186
Thus, Simple Interest = $3186
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 × 3186/5900 × 9
= 318600/53100
= 6 years (using formula)
Thus, Time (T) = 6 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) = $5900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3186 (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 $5900
= 9/100 × 5900
= 9 × 5900/100
= 53100/100 = 531
Thus, simple Interest for 1 year = $531
Now,
∵ If the simple Interest is $531, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/531 years
∴ If the simple Interest is $3186, then the time = 1/531 × 3186 years
= 1 × 3186/531 years
= 3186/531 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 7% simple interest?
(4) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(9) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?