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) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(4) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?
(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.