Question:
Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4300
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7740
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 = $7740 – $4300 = $3440
Thus, Simple Interest = $3440
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 × 3440/4300 × 10
= 344000/43000
= 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) = $4300
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $3440 (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 = 10% of Principal
= 10% of $4300
= 10/100 × 4300
= 10 × 4300/100
= 43000/100 = 430
Thus, simple Interest for 1 year = $430
Now,
∵ If the simple Interest is $430, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/430 years
∴ If the simple Interest is $3440, then the time = 1/430 × 3440 years
= 1 × 3440/430 years
= 3440/430 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(8) Jessica had to pay $4312.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.