Question:
Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10432
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 = $10432 – $6400 = $4032
Thus, Simple Interest = $4032
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 × 4032/6400 × 7
= 403200/44800
= 9 years (using formula)
Thus, Time (T) = 9 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) = $6400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4032 (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 $6400
= 7/100 × 6400
= 7 × 6400/100
= 44800/100 = 448
Thus, simple Interest for 1 year = $448
Now,
∵ If the simple Interest is $448, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/448 years
∴ If the simple Interest is $4032, then the time = 1/448 × 4032 years
= 1 × 4032/448 years
= 4032/448 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(4) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?
(10) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.