Question:
Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8944
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 = $8944 – $5200 = $3744
Thus, Simple Interest = $3744
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 × 3744/5200 × 9
= 374400/46800
= 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) = $5200
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3744 (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 = 9% of Principal
= 9% of $5200
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = 468
Thus, simple Interest for 1 year = $468
Now,
∵ If the simple Interest is $468, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/468 years
∴ If the simple Interest is $3744, then the time = 1/468 × 3744 years
= 1 × 3744/468 years
= 3744/468 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(2) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 6% simple interest?
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(10) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.