Question:
Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6600
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10296
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 = $10296 – $6600 = $3696
Thus, Simple Interest = $3696
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 × 3696/6600 × 7
= 369600/46200
= 8 years (using formula)
Thus, Time (T) = 8 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 = $3696 (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 $3696, then the time = 1/462 × 3696 years
= 1 × 3696/462 years
= 3696/462 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Donna paid $5432 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 does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?
(4) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.
(6) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
(10) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?