Question:
William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7450
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 = $7450 – $5000 = $2450
Thus, Simple Interest = $2450
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 × 2450/5000 × 7
= 245000/35000
= 7 years (using formula)
Thus, Time (T) = 7 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) = $5000
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2450 (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 $5000
= 7/100 × 5000
= 7 × 5000/100
= 35000/100 = 350
Thus, simple Interest for 1 year = $350
Now,
∵ If the simple Interest is $350, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/350 years
∴ If the simple Interest is $2450, then the time = 1/350 × 2450 years
= 1 × 2450/350 years
= 2450/350 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(4) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(8) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.