Question:
How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?
Correct Answer
$6850
Solution And Explanation
Solution
Given,
Amount (A) = $8562.5
Rate of Simple Interest (R) = 5%
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
$8562.5 = P (1 + 5% × 5)
⇒ $8562.5 = P (1 + 5/100 × 5)
⇒ $8562.5 = P (1 + 5 × 5/100)
⇒ $8562.5 = P (1 + 25/100)
⇒ $8562.5 = P (100 + 25/100)
⇒ $8562.5 = P × 125/100
⇒ P × 125/100 = $8562.5
⇒ P = 8562.5/125/100
⇒ P = 8562.5 × 100/125
⇒ P = 8562.5 × 100/125
⇒ P = 856250/125
⇒ P = $6850
Thus, the sum borrowed (P) = $6850 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 8562.5, then the Principal = 100/125 × 8562.5
= 100 × 8562.5/125
= 856250/125
= 6850
Thus, Principal = $6850
Thus, the sum borrowed = $6850 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(6) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?