Question:
Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $12920
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 = $12920 – $6800 = $6120
Thus, Simple Interest = $6120
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 × 6120/6800 × 9
= 612000/61200
= 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) = $6800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $6120 (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 $6120, then the time = 1/612 × 6120 years
= 1 × 6120/612 years
= 6120/612 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% 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) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(8) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 6% simple interest?