Question:
Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $9384
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 = $9384 – $6900 = $2484
Thus, Simple Interest = $2484
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 × 2484/6900 × 6
= 248400/41400
= 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) = $6900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2484 (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 $6900
= 6/100 × 6900
= 6 × 6900/100
= 41400/100 = 414
Thus, simple Interest for 1 year = $414
Now,
∵ If the simple Interest is $414, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/414 years
∴ If the simple Interest is $2484, then the time = 1/414 × 2484 years
= 1 × 2484/414 years
= 2484/414 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(2) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(5) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(6) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.
(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(9) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.