Question:
Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $8584
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 = $8584 – $5800 = $2784
Thus, Simple Interest = $2784
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 × 2784/5800 × 8
= 278400/46400
= 6 years (using formula)
Thus, Time (T) = 6 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) = $5800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2784 (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 = 8% of Principal
= 8% of $5800
= 8/100 × 5800
= 8 × 5800/100
= 46400/100 = 464
Thus, simple Interest for 1 year = $464
Now,
∵ If the simple Interest is $464, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/464 years
∴ If the simple Interest is $2784, then the time = 1/464 × 2784 years
= 1 × 2784/464 years
= 2784/464 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.
(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(9) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?