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 Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(3) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(9) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.