Question:
Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4700
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $7520
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 = $7520 – $4700 = $2820
Thus, Simple Interest = $2820
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 × 2820/4700 × 10
= 282000/47000
= 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) = $4700
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $2820 (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 = 10% of Principal
= 10% of $4700
= 10/100 × 4700
= 10 × 4700/100
= 47000/100 = 470
Thus, simple Interest for 1 year = $470
Now,
∵ If the simple Interest is $470, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/470 years
∴ If the simple Interest is $2820, then the time = 1/470 × 2820 years
= 1 × 2820/470 years
= 2820/470 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) If Matthew paid $4704 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 James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(3) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(4) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?
(6) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?