Question:
Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7897
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 = $7897 – $5300 = $2597
Thus, Simple Interest = $2597
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 × 2597/5300 × 7
= 259700/37100
= 7 years (using formula)
Thus, Time (T) = 7 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) = 7% per annum
Simple Interest = $2597 (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 $5300
= 7/100 × 5300
= 7 × 5300/100
= 37100/100 = 371
Thus, simple Interest for 1 year = $371
Now,
∵ If the simple Interest is $371, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/371 years
∴ If the simple Interest is $2597, then the time = 1/371 × 2597 years
= 1 × 2597/371 years
= 2597/371 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
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(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) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(7) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?