Question:
Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8869
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 = $8869 – $4900 = $3969
Thus, Simple Interest = $3969
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 × 3969/4900 × 9
= 396900/44100
= 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) = $4900
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3969 (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 = 9% of Principal
= 9% of $4900
= 9/100 × 4900
= 9 × 4900/100
= 44100/100 = 441
Thus, simple Interest for 1 year = $441
Now,
∵ If the simple Interest is $441, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/441 years
∴ If the simple Interest is $3969, then the time = 1/441 × 3969 years
= 1 × 3969/441 years
= 3969/441 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 3 years.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
(8) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.