Question:
Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $8840
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 = $8840 – $6500 = $2340
Thus, Simple Interest = $2340
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 × 2340/6500 × 6
= 234000/39000
= 6 years (using formula)
Thus, Time (T) = 6 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) = 6% per annum
Simple Interest = $2340 (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 = 6% of Principal
= 6% of $6500
= 6/100 × 6500
= 6 × 6500/100
= 39000/100 = 390
Thus, simple Interest for 1 year = $390
Now,
∵ If the simple Interest is $390, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/390 years
∴ If the simple Interest is $2340, then the time = 1/390 × 2340 years
= 1 × 2340/390 years
= 2340/390 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.
(5) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(8) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.