Question:
( 1 of 10 ) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.
(A) 711
(B) 712
(C) 1415
(D) 710
You selected
13.5
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9291
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 = $9291 – $5700 = $3591
Thus, Simple Interest = $3591
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 × 3591/5700 × 7
= 359100/39900
= 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) = 7% per annum
Simple Interest = $3591 (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 $5700
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = 399
Thus, simple Interest for 1 year = $399
Now,
∵ If the simple Interest is $399, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/399 years
∴ If the simple Interest is $3591, then the time = 1/399 × 3591 years
= 1 × 3591/399 years
= 3591/399 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.
(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(3) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(6) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(9) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.