Question:
Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10260
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 = $10260 – $5400 = $4860
Thus, Simple Interest = $4860
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 × 4860/5400 × 9
= 486000/48600
= 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) = $5400
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4860 (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 $5400
= 9/100 × 5400
= 9 × 5400/100
= 48600/100 = 486
Thus, simple Interest for 1 year = $486
Now,
∵ If the simple Interest is $486, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/486 years
∴ If the simple Interest is $4860, then the time = 1/486 × 4860 years
= 1 × 4860/486 years
= 4860/486 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(2) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(6) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(9) 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.
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.