Question:
( 1 of 10 ) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9632 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) = $5600
Rate of Simple Interest (R) = 9% per annum
Amount (A) = $9632
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 = $9632 – $5600 = $4032
Thus, Simple Interest = $4032
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 × 4032/5600 × 9
= 403200/50400
= 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) = $5600
Rate of Simple Interest (R) = 9% per annum
Simple Interest = $4032 (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 = 9% of Principal
= 9% of $5600
= 9/100 × 5600
= 9 × 5600/100
= 50400/100 = 504
Thus, simple Interest for 1 year = $504
Now,
∵ If the simple Interest is $504, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/504 years
∴ If the simple Interest is $4032, then the time = 1/504 × 4032 years
= 1 × 4032/504 years
= 4032/504 = 8 years
Thus, time (T) = 8 years Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(3) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(5) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(9) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?