Question:
Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10080
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 = $10080 – $5600 = $4480
Thus, Simple Interest = $4480
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 × 4480/5600 × 8
= 448000/44800
= 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) = $5600
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4480 (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 $5600
= 8/100 × 5600
= 8 × 5600/100
= 44800/100 = 448
Thus, simple Interest for 1 year = $448
Now,
∵ If the simple Interest is $448, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/448 years
∴ If the simple Interest is $4480, then the time = 1/448 × 4480 years
= 1 × 4480/448 years
= 4480/448 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
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(2) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(6) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(10) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.