Question:
How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
Correct Answer
$5350
Solution And Explanation
Solution
Given,
Amount (A) = $5885
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
$5885 = P (1 + 2% × 5)
⇒ $5885 = P (1 + 2/100 × 5)
⇒ $5885 = P (1 + 2 × 5/100)
⇒ $5885 = P (1 + 10/100)
⇒ $5885 = P (100 + 10/100)
⇒ $5885 = P × 110/100
⇒ P × 110/100 = $5885
⇒ P = 5885/110/100
⇒ P = 5885 × 100/110
⇒ P = 5885 × 100/110
⇒ P = 588500/110
⇒ P = $5350
Thus, the sum borrowed (P) = $5350 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 5885, then the Principal = 100/110 × 5885
= 100 × 5885/110
= 588500/110
= 5350
Thus, Principal = $5350
Thus, the sum borrowed = $5350 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(4) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.
(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.