Question:
Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4200
Rate of Simple Interest (R) = 10% per annum
Amount (A) = $6720
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 = $6720 – $4200 = $2520
Thus, Simple Interest = $2520
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 × 2520/4200 × 10
= 252000/42000
= 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) = $4200
Rate of Simple Interest (R) = 10% per annum
Simple Interest = $2520 (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 $4200
= 10/100 × 4200
= 10 × 4200/100
= 42000/100 = 420
Thus, simple Interest for 1 year = $420
Now,
∵ If the simple Interest is $420, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/420 years
∴ If the simple Interest is $2520, then the time = 1/420 × 2520 years
= 1 × 2520/420 years
= 2520/420 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(4) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
(6) 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.
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(8) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(9) 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.
(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.