Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $8107.5

Rate of Simple Interest (R) = 3%

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

$8107.5 = P (1 + 3% × 5)

⇒ $8107.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8107.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8107.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8107.5 = P (^{100 + 15}/₁₀₀)

⇒ $8107.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8107.5

⇒ P = ^8107.5/_¹¹⁵/100

⇒ P = 8107.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8107.5 × 100}/₁₁₅

⇒ P = ⁸¹⁰⁷⁵⁰/₁₁₅

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8107.5, then the Principal = ¹⁰⁰/₁₁₅ × 8107.5

= ^{100 × 8107.5}/₁₁₅

= ⁸¹⁰⁷⁵⁰/₁₁₅

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(5) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.

(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.

(10) 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.