Question:
Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $8480
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 = $8480 – $5300 = $3180
Thus, Simple Interest = $3180
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 × 3180/5300 × 10
= 318000/53000
= 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) = $5300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3180 (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 = 10% of Principal
= 10% of $5300
= 10/100 × 5300
= 10 × 5300/100
= 53000/100 = 530
Thus, simple Interest for 1 year = $530
Now,
∵ If the simple Interest is $530, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/530 years
∴ If the simple Interest is $3180, then the time = 1/530 × 3180 years
= 1 × 3180/530 years
= 3180/530 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?
(2) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(5) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.