Question:
Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 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) = 6% per annum
Amount (A) = $7992
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 = $7992 – $5400 = $2592
Thus, Simple Interest = $2592
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 × 2592/5400 × 6
= 259200/32400
= 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) = 6% per annum
Simple Interest = $2592 (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 = 6% of Principal
= 6% of $5400
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = 324
Thus, simple Interest for 1 year = $324
Now,
∵ If the simple Interest is $324, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/324 years
∴ If the simple Interest is $2592, then the time = 1/324 × 2592 years
= 1 × 2592/324 years
= 2592/324 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(3) Nancy had to pay $4523.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(5) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?
(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?
(8) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.