Question:
Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9288
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 = $9288 – $5400 = $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 × 3888/5400 × 9
= 388800/48600
= 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) = $5400
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 $5400
= 9/100 × 5400
= 9 × 5400/100
= 48600/100 = 486
Thus, simple Interest for 1 year = $486
Now,
∵ If the simple Interest is $486, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/486 years
∴ If the simple Interest is $3888, then the time = 1/486 × 3888 years
= 1 × 3888/486 years
= 3888/486 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(3) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(6) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(10) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.