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) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.

(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.