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 Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(3) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(6) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(10) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.