Question:
Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $9048
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 = $9048 – $5800 = $3248
Thus, Simple Interest = $3248
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 × 3248/5800 × 8
= 324800/46400
= 7 years (using formula)
Thus, Time (T) = 7 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 = $3248 (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 $3248, then the time = 1/464 × 3248 years
= 1 × 3248/464 years
= 3248/464 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(3) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.
(10) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.