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) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(3) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?
(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.
(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.