Simple Interest
Math MCQs

Question :    How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

Correct Answer  $5800

Solution & Explanation

Solution

Given,

Amount (A) = $7250

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

$7250 = P (1 + 5% × 5)

⇒ $7250 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7250 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7250 = P (1 + ²⁵/₁₀₀)

⇒ $7250 = P (^{100 + 25}/₁₀₀)

⇒ $7250 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7250

⇒ P = ⁷²⁵⁰/_¹²⁵/100

⇒ P = 7250 × ¹⁰⁰/₁₂₅

⇒ P = ^{7250 × 100}/₁₂₅

⇒ P = ⁷²⁵⁰⁰⁰/₁₂₅

⇒ P = $5800

Thus, the sum borrowed (P) = $5800 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 7250, then the Principal = ¹⁰⁰/₁₂₅ × 7250

= ^{100 × 7250}/₁₂₅

= ⁷²⁵⁰⁰⁰/₁₂₅

= 5800

Thus, Principal = $5800

Thus, the sum borrowed = $5800 Answer

Similar Questions

(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?

(5) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.

(6) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.

(9) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.