Question:
How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
Correct Answer
$6100
Solution And Explanation
Solution
Given,
Amount (A) = $7320
Rate of Simple Interest (R) = 4%
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
$7320 = P (1 + 4% × 5)
⇒ $7320 = P (1 + 4/100 × 5)
⇒ $7320 = P (1 + 4 × 5/100)
⇒ $7320 = P (1 + 20/100)
⇒ $7320 = P (100 + 20/100)
⇒ $7320 = P × 120/100
⇒ P × 120/100 = $7320
⇒ P = 7320/120/100
⇒ P = 7320 × 100/120
⇒ P = 7320 × 100/120
⇒ P = 732000/120
⇒ P = $6100
Thus, the sum borrowed (P) = $6100 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 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 7320, then the Principal = 100/120 × 7320
= 100 × 7320/120
= 732000/120
= 6100
Thus, Principal = $6100
Thus, the sum borrowed = $6100 Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 8 years.
(4) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(6) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?