Question:
Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4505
Rate of Simple Interest (R) = 2%
Time (T) = 3 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
$4505 = P (1 + 2% × 3)
⇒ $4505 = P (1 + 2/100 × 3)
⇒ $4505 = P (1 + 2 × 3/100)
⇒ $4505 = P (1 + 6/100)
⇒ $4505 = P (100 + 6/100)
⇒ $4505 = P × 106/100
⇒ P × 106/100 = $4505
⇒ P = 4505/106/100
⇒ P = 4505 × 100/106
⇒ P = 4505 × 100/106
⇒ P = 450500/106
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4505, then the Principal = 100/106 × 4505
= 100 × 4505/106
= 450500/106
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) 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.
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?
(4) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 8 years.
(7) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?