Simple Interest
Math MCQs

Question :    How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?

Correct Answer  $6500

Solution & Explanation

Solution

Given,

Amount (A) = $7150

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

$7150 = P (1 + 2% × 5)

⇒ $7150 = P (1 + ²/₁₀₀ × 5)

⇒ $7150 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7150 = P (1 + ¹⁰/₁₀₀)

⇒ $7150 = P (^{100 + 10}/₁₀₀)

⇒ $7150 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7150

⇒ P = ⁷¹⁵⁰/_¹¹⁰/100

⇒ P = 7150 × ¹⁰⁰/₁₁₀

⇒ P = ^{7150 × 100}/₁₁₀

⇒ P = ⁷¹⁵⁰⁰⁰/₁₁₀

⇒ P = $6500

Thus, the sum borrowed (P) = $6500 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 7150, then the Principal = ¹⁰⁰/₁₁₀ × 7150

= ^{100 × 7150}/₁₁₀

= ⁷¹⁵⁰⁰⁰/₁₁₀

= 6500

Thus, Principal = $6500

Thus, the sum borrowed = $6500 Answer

Similar Questions

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

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

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

(4) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?

(9) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?