Question:
How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Amount (A) = $6160
Rate of Simple Interest (R) = 2%
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
$6160 = P (1 + 2% × 5)
⇒ $6160 = P (1 + 2/100 × 5)
⇒ $6160 = P (1 + 2 × 5/100)
⇒ $6160 = P (1 + 10/100)
⇒ $6160 = P (100 + 10/100)
⇒ $6160 = P × 110/100
⇒ P × 110/100 = $6160
⇒ P = 6160/110/100
⇒ P = 6160 × 100/110
⇒ P = 6160 × 100/110
⇒ P = 616000/110
⇒ P = $5600
Thus, the sum borrowed (P) = $5600 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 6160, then the Principal = 100/110 × 6160
= 100 × 6160/110
= 616000/110
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?