Question:
Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9976
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 = $9976 – $5800 = $4176
Thus, Simple Interest = $4176
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 × 4176/5800 × 8
= 417600/46400
= 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) = $5800
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $4176 (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 $4176, then the time = 1/464 × 4176 years
= 1 × 4176/464 years
= 4176/464 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(3) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 3 years.
(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?