Question:
Patricia took a loan of $4300 at the rate of 9% 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
7
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 9% 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 × 9
= 270900/38700
= 7 years (using formula)
Thus, Time (T) = 7 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) = 9% 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 = 9% of Principal
= 9% of $4300
= 9/100 × 4300
= 9 × 4300/100
= 38700/100 = 387
Thus, simple Interest for 1 year = $387
Now,
∵ If the simple Interest is $387, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/387 years
∴ If the simple Interest is $2709, then the time = 1/387 × 2709 years
= 1 × 2709/387 years
= 2709/387 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?
(7) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.