Question:
Betty took a loan of $6500 at the rate of 8% 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
10
Solution And Explanation
Solution
Given,
Principal (P) = $6500
Rate of Simple Interest (R) = 8% 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 × 8
= 520000/52000
= 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) = 8% 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 = 8% of Principal
= 8% of $6500
= 8/100 × 6500
= 8 × 6500/100
= 52000/100 = 520
Thus, simple Interest for 1 year = $520
Now,
∵ If the simple Interest is $520, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/520 years
∴ If the simple Interest is $5200, then the time = 1/520 × 5200 years
= 1 × 5200/520 years
= 5200/520 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(6) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.