Question:
Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $11700
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 = $11700 – $6500 = $5200
Thus, Simple Interest = $5200
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 × 5200/6500 × 10
= 520000/65000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $6500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5200 (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 $6500
= 10/100 × 6500
= 10 × 6500/100
= 65000/100 = 650
Thus, simple Interest for 1 year = $650
Now,
∵ If the simple Interest is $650, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/650 years
∴ If the simple Interest is $5200, then the time = 1/650 × 5200 years
= 1 × 5200/650 years
= 5200/650 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(4) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(5) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(9) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.