Question:
How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?
Correct Answer
$6650
Solution And Explanation
Solution
Given,
Amount (A) = $8312.5
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
$8312.5 = P (1 + 5% × 5)
⇒ $8312.5 = P (1 + 5/100 × 5)
⇒ $8312.5 = P (1 + 5 × 5/100)
⇒ $8312.5 = P (1 + 25/100)
⇒ $8312.5 = P (100 + 25/100)
⇒ $8312.5 = P × 125/100
⇒ P × 125/100 = $8312.5
⇒ P = 8312.5/125/100
⇒ P = 8312.5 × 100/125
⇒ P = 8312.5 × 100/125
⇒ P = 831250/125
⇒ P = $6650
Thus, the sum borrowed (P) = $6650 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 8312.5, then the Principal = 100/125 × 8312.5
= 100 × 8312.5/125
= 831250/125
= 6650
Thus, Principal = $6650
Thus, the sum borrowed = $6650 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(3) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(7) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?