Question:
Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $6400
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $10880
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 = $10880 – $6400 = $4480
Thus, Simple Interest = $4480
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 × 4480/6400 × 7
= 448000/44800
= 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) = $6400
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $4480 (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 $4480, then the time = 1/448 × 4480 years
= 1 × 4480/448 years
= 4480/448 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.
(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(9) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(10) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.