Question:
Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12308
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 = $12308 – $6800 = $5508
Thus, Simple Interest = $5508
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 × 5508/6800 × 9
= 550800/61200
= 9 years (using formula)
Thus, Time (T) = 9 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 = $5508 (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 $5508, then the time = 1/612 × 5508 years
= 1 × 5508/612 years
= 5508/612 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(3) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(8) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 7 years.
(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.