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) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(4) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?