Question:
( 1 of 10 ) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
12
Correct Answer
8
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (R) = 8% per annum
Amount (A) = $6560
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 = $6560 – $4000 = $2560
Thus, Simple Interest = $2560
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 × 2560/4000 × 8
= 256000/32000
= 8 years (using formula)
Thus, Time (T) = 8 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) = $4000
Rate of Simple Interest (R) = 8% per annum
Simple Interest = $2560 (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 $4000
= 8/100 × 4000
= 8 × 4000/100
= 32000/100 = 320
Thus, simple Interest for 1 year = $320
Now,
∵ If the simple Interest is $320, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/320 years
∴ If the simple Interest is $2560, then the time = 1/320 × 2560 years
= 1 × 2560/320 years
= 2560/320 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(4) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(10) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?