Question:
Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9120
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 = $9120 – $5700 = $3420
Thus, Simple Interest = $3420
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 × 3420/5700 × 6
= 342000/34200
= 10 years (using formula)
Thus, Time (T) = 10 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) = 6% per annum
Simple Interest = $3420 (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 = 6% of Principal
= 6% of $5700
= 6/100 × 5700
= 6 × 5700/100
= 34200/100 = 342
Thus, simple Interest for 1 year = $342
Now,
∵ If the simple Interest is $342, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/342 years
∴ If the simple Interest is $3420, then the time = 1/342 × 3420 years
= 1 × 3420/342 years
= 3420/342 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(4) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(6) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?
(8) Thomas had to pay $4028 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.