Question:
If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4600
Solution And Explanation
Solution
Given,
Amount (A) = $5520
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$5520 = P (1 + 5% × 4)
⇒ $5520 = P (1 + 5/100 × 4)
⇒ $5520 = P (1 + 5 × 4/100)
⇒ $5520 = P (1 + 20/100)
⇒ $5520 = P (100 + 20/100)
⇒ $5520 = P × 120/100
⇒ P × 120/100 = $5520
⇒ P = 5520/120/100
⇒ P = 5520 × 100/120
⇒ P = 5520 × 100/120
⇒ P = 552000/120
⇒ P = $4600
Thus, the sum borrowed (P) = $4600 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 5520, then the Principal = 100/120 × 5520
= 100 × 5520/120
= 552000/120
= 4600
Thus, Principal = $4600
Thus, the sum borrowed = $4600 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.