Question:
Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7844
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 = $7844 – $5300 = $2544
Thus, Simple Interest = $2544
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 × 2544/5300 × 6
= 254400/31800
= 8 years (using formula)
Thus, Time (T) = 8 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) = $5300
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2544 (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 $5300
= 6/100 × 5300
= 6 × 5300/100
= 31800/100 = 318
Thus, simple Interest for 1 year = $318
Now,
∵ If the simple Interest is $318, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/318 years
∴ If the simple Interest is $2544, then the time = 1/318 × 2544 years
= 1 × 2544/318 years
= 2544/318 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(3) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?
(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.