Question:
Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $11868
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 = $11868 – $6900 = $4968
Thus, Simple Interest = $4968
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 × 4968/6900 × 9
= 496800/62100
= 8 years (using formula)
Thus, Time (T) = 8 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) = 9% per annum
Simple Interest = $4968 (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 = 9% of Principal
= 9% of $6900
= 9/100 × 6900
= 9 × 6900/100
= 62100/100 = 621
Thus, simple Interest for 1 year = $621
Now,
∵ If the simple Interest is $621, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/621 years
∴ If the simple Interest is $4968, then the time = 1/621 × 4968 years
= 1 × 4968/621 years
= 4968/621 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(5) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(10) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.