Simple Interest
Math MCQs

Question :    How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

Correct Answer  $6650

Solution & Explanation

Solution

Given,

Amount (A) = $7315

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

$7315 = P (1 + 2% × 5)

⇒ $7315 = P (1 + ²/₁₀₀ × 5)

⇒ $7315 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7315 = P (1 + ¹⁰/₁₀₀)

⇒ $7315 = P (^{100 + 10}/₁₀₀)

⇒ $7315 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7315

⇒ P = ⁷³¹⁵/_¹¹⁰/100

⇒ P = 7315 × ¹⁰⁰/₁₁₀

⇒ P = ^{7315 × 100}/₁₁₀

⇒ P = ⁷³¹⁵⁰⁰/₁₁₀

⇒ P = $6650

Thus, the sum borrowed (P) = $6650 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 7315, then the Principal = ¹⁰⁰/₁₁₀ × 7315

= ^{100 × 7315}/₁₁₀

= ⁷³¹⁵⁰⁰/₁₁₀

= 6650

Thus, Principal = $6650

Thus, the sum borrowed = $6650 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(5) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.

(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(9) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.