Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6687.5

Rate of Simple Interest (R) = 5%

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

$6687.5 = P (1 + 5% × 5)

⇒ $6687.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6687.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6687.5 = P (1 + ²⁵/₁₀₀)

⇒ $6687.5 = P (^{100 + 25}/₁₀₀)

⇒ $6687.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6687.5

⇒ P = ^6687.5/_¹²⁵/100

⇒ P = 6687.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6687.5 × 100}/₁₂₅

⇒ P = ⁶⁶⁸⁷⁵⁰/₁₂₅

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6687.5, then the Principal = ¹⁰⁰/₁₂₅ × 6687.5

= ^{100 × 6687.5}/₁₂₅

= ⁶⁶⁸⁷⁵⁰/₁₂₅

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(5) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.

(7) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(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) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?