Question:
How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
Correct Answer
$5550
Solution And Explanation
Solution
Given,
Amount (A) = $6660
Rate of Simple Interest (R) = 4%
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
$6660 = P (1 + 4% × 5)
⇒ $6660 = P (1 + 4/100 × 5)
⇒ $6660 = P (1 + 4 × 5/100)
⇒ $6660 = P (1 + 20/100)
⇒ $6660 = P (100 + 20/100)
⇒ $6660 = P × 120/100
⇒ P × 120/100 = $6660
⇒ P = 6660/120/100
⇒ P = 6660 × 100/120
⇒ P = 6660 × 100/120
⇒ P = 666000/120
⇒ P = $5550
Thus, the sum borrowed (P) = $5550 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6660, then the Principal = 100/120 × 6660
= 100 × 6660/120
= 666000/120
= 5550
Thus, Principal = $5550
Thus, the sum borrowed = $5550 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.
(5) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?
(7) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.