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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?

(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.

(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.

(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.

(6) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 8% simple interest?

(8) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.