Question:
Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
Correct Answer
7
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $10764
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 = $10764 – $6900 = $3864
Thus, Simple Interest = $3864
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 × 3864/6900 × 8
= 386400/55200
= 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) = $6900
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $3864 (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 $6900
= 8/100 × 6900
= 8 × 6900/100
= 55200/100 = 552
Thus, simple Interest for 1 year = $552
Now,
∵ If the simple Interest is $552, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/552 years
∴ If the simple Interest is $3864, then the time = 1/552 × 3864 years
= 1 × 3864/552 years
= 3864/552 = 7 years
Thus, time (T) = 7 years Answer
Similar Questions
(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(4) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(8) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.