Question:
Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9804
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 = $9804 – $5700 = $4104
Thus, Simple Interest = $4104
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 × 4104/5700 × 8
= 410400/45600
= 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) = $5700
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4104 (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 $5700
= 8/100 × 5700
= 8 × 5700/100
= 45600/100 = 456
Thus, simple Interest for 1 year = $456
Now,
∵ If the simple Interest is $456, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/456 years
∴ If the simple Interest is $4104, then the time = 1/456 × 4104 years
= 1 × 4104/456 years
= 4104/456 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(3) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?
(6) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(8) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.