Question:
( 1 of 10 ) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(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
$6476.25
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $8635
Rate of Simple Interest (R) = 2%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$8635 = P (1 + 2% × 5)
⇒ $8635 = P (1 + 2/100 × 5)
⇒ $8635 = P (1 + 2 × 5/100)
⇒ $8635 = P (1 + 10/100)
⇒ $8635 = P (100 + 10/100)
⇒ $8635 = P × 110/100
⇒ P × 110/100 = $8635
⇒ P = 8635/110/100
⇒ P = 8635 × 100/110
⇒ P = 8635 × 100/110
⇒ P = 863500/110
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8635, then the Principal = 100/110 × 8635
= 100 × 8635/110
= 863500/110
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(3) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?
(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.