Question:
Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $12350
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 = $12350 – $6500 = $5850
Thus, Simple Interest = $5850
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 × 5850/6500 × 10
= 585000/65000
= 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) = $6500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $5850 (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 $5850, then the time = 1/650 × 5850 years
= 1 × 5850/650 years
= 5850/650 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 8 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.
(3) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(6) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.