Question:
Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6200
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9548
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 = $9548 – $6200 = $3348
Thus, Simple Interest = $3348
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 × 3348/6200 × 6
= 334800/37200
= 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) = $6200
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3348 (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 = 6% of Principal
= 6% of $6200
= 6/100 × 6200
= 6 × 6200/100
= 37200/100 = 372
Thus, simple Interest for 1 year = $372
Now,
∵ If the simple Interest is $372, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/372 years
∴ If the simple Interest is $3348, then the time = 1/372 × 3348 years
= 1 × 3348/372 years
= 3348/372 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(2) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.