Question:
Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $7384
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 = $7384 – $5200 = $2184
Thus, Simple Interest = $2184
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 × 2184/5200 × 7
= 218400/36400
= 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) = $5200
Rate of Simple Interest (R) = 7% per annum
Simple Interest = $2184 (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 $5200
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = 364
Thus, simple Interest for 1 year = $364
Now,
∵ If the simple Interest is $364, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/364 years
∴ If the simple Interest is $2184, then the time = 1/364 × 2184 years
= 1 × 2184/364 years
= 2184/364 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(2) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(4) Sandra had to pay $4984 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.