Question:
Sandra took a loan of $6900 at the rate of 8% 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
9
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 8% 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 × 8
= 496800/55200
= 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) = $6900
Rate of Simple Interest (R) = 8% 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 = 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 $4968, then the time = 1/552 × 4968 years
= 1 × 4968/552 years
= 4968/552 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(3) David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(5) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.
(6) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?
(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(8) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.