Question:
Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $10472
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 = $10472 – $6800 = $3672
Thus, Simple Interest = $3672
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 × 3672/6800 × 9
= 367200/61200
= 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) = $6800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3672 (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 $6800
= 9/100 × 6800
= 9 × 6800/100
= 61200/100 = 612
Thus, simple Interest for 1 year = $612
Now,
∵ If the simple Interest is $612, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/612 years
∴ If the simple Interest is $3672, then the time = 1/612 × 3672 years
= 1 × 3672/612 years
= 3672/612 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.
(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(8) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?