Question:
David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
Correct Answer
6
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $7104
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 = $7104 – $4800 = $2304
Thus, Simple Interest = $2304
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 × 2304/4800 × 8
= 230400/38400
= 6 years (using formula)
Thus, Time (T) = 6 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) = 8% per annum
Simple Interest = $2304 (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 $4800
= 8/100 × 4800
= 8 × 4800/100
= 38400/100 = 384
Thus, simple Interest for 1 year = $384
Now,
∵ If the simple Interest is $384, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/384 years
∴ If the simple Interest is $2304, then the time = 1/384 × 2304 years
= 1 × 2304/384 years
= 2304/384 = 6 years
Thus, time (T) = 6 years Answer
Similar Questions
(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(3) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?
(4) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(8) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.