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) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(5) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?
(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(10) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?