Question:
David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $7392
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 = $7392 – $4800 = $2592
Thus, Simple Interest = $2592
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 × 2592/4800 × 6
= 259200/28800
= 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) = $4800
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $2592 (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 $4800
= 6/100 × 4800
= 6 × 4800/100
= 28800/100 = 288
Thus, simple Interest for 1 year = $288
Now,
∵ If the simple Interest is $288, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/288 years
∴ If the simple Interest is $2592, then the time = 1/288 × 2592 years
= 1 × 2592/288 years
= 2592/288 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) 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.
(2) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(8) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?