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) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 9% simple interest?

(6) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

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

(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?

(9) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.