Question:
Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7009
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 = $7009 – $4300 = $2709
Thus, Simple Interest = $2709
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 × 2709/4300 × 7
= 270900/30100
= 9 years (using formula)
Thus, Time (T) = 9 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) = $4300
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2709 (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 = 7% of Principal
= 7% of $4300
= 7/100 × 4300
= 7 × 4300/100
= 30100/100 = 301
Thus, simple Interest for 1 year = $301
Now,
∵ If the simple Interest is $301, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/301 years
∴ If the simple Interest is $2709, then the time = 1/301 × 2709 years
= 1 × 2709/301 years
= 2709/301 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
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(2) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.