Question:
Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $13000
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 = $13000 – $6500 = $6500
Thus, Simple Interest = $6500
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 × 6500/6500 × 10
= 650000/65000
= 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) = $6500
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $6500 (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 $6500, then the time = 1/650 × 6500 years
= 1 × 6500/650 years
= 6500/650 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
(3) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(5) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.