Question:
Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $9372
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 = $9372 – $6600 = $2772
Thus, Simple Interest = $2772
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 × 2772/6600 × 7
= 277200/46200
= 6 years (using formula)
Thus, Time (T) = 6 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) = $6600
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2772 (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 $6600
= 7/100 × 6600
= 7 × 6600/100
= 46200/100 = 462
Thus, simple Interest for 1 year = $462
Now,
∵ If the simple Interest is $462, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/462 years
∴ If the simple Interest is $2772, then the time = 1/462 × 2772 years
= 1 × 2772/462 years
= 2772/462 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(3) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.
(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?