Question:
David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $8688
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 = $8688 – $4800 = $3888
Thus, Simple Interest = $3888
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 × 3888/4800 × 9
= 388800/43200
= 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) = $4800
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $3888 (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 $3888, then the time = 1/432 × 3888 years
= 1 × 3888/432 years
= 3888/432 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(9) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.