Question:
David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
Correct Answer
10
Solution And Explanation
Solution
Given,
Principal (P) = $4800
Rate of Simple Interest (R) = 7% per annum
Amount (A) = $8160
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 = $8160 – $4800 = $3360
Thus, Simple Interest = $3360
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 × 3360/4800 × 7
= 336000/33600
= 10 years (using formula)
Thus, Time (T) = 10 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) = 7% per annum
Simple Interest = $3360 (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 = 7% of Principal
= 7% of $4800
= 7/100 × 4800
= 7 × 4800/100
= 33600/100 = 336
Thus, simple Interest for 1 year = $336
Now,
∵ If the simple Interest is $336, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/336 years
∴ If the simple Interest is $3360, then the time = 1/336 × 3360 years
= 1 × 3360/336 years
= 3360/336 = 10 years
Thus, time (T) = 10 years Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.
(8) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(9) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?
(10) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?