Question:
David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $7824
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 = $7824 – $4800 = $3024
Thus, Simple Interest = $3024
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 × 3024/4800 × 9
= 302400/43200
= 7 years (using formula)
Thus, Time (T) = 7 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) = $4800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3024 (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 $4800
= 9/100 × 4800
= 9 × 4800/100
= 43200/100 = 432
Thus, simple Interest for 1 year = $432
Now,
∵ If the simple Interest is $432, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/432 years
∴ If the simple Interest is $3024, then the time = 1/432 × 3024 years
= 1 × 3024/432 years
= 3024/432 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.
(6) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.