Question:
How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
Correct Answer
$6950
Solution And Explanation
Solution
Given,
Amount (A) = $7645
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
$7645 = P (1 + 2% × 5)
⇒ $7645 = P (1 + 2/100 × 5)
⇒ $7645 = P (1 + 2 × 5/100)
⇒ $7645 = P (1 + 10/100)
⇒ $7645 = P (100 + 10/100)
⇒ $7645 = P × 110/100
⇒ P × 110/100 = $7645
⇒ P = 7645/110/100
⇒ P = 7645 × 100/110
⇒ P = 7645 × 100/110
⇒ P = 764500/110
⇒ P = $6950
Thus, the sum borrowed (P) = $6950 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 7645, then the Principal = 100/110 × 7645
= 100 × 7645/110
= 764500/110
= 6950
Thus, Principal = $6950
Thus, the sum borrowed = $6950 Answer
Similar Questions
(1) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.
(2) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(4) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(8) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?