Question:
Mark took a loan of $6800 at the rate of 10% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $6800
Rate of Simple Interest (R) = 10% 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 × 10
= 612000/68000
= 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) = 10% 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 = 10% of Principal
= 10% of $6800
= 10/100 × 6800
= 10 × 6800/100
= 68000/100 = 680
Thus, simple Interest for 1 year = $680
Now,
∵ If the simple Interest is $680, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/680 years
∴ If the simple Interest is $6120, then the time = 1/680 × 6120 years
= 1 × 6120/680 years
= 6120/680 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(2) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(4) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 2% simple interest?
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.