Simple Interest
Math MCQs

Question :    How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

Correct Answer  $7300

Solution & Explanation

Solution

Given,

Amount (A) = $9125

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

$9125 = P (1 + 5% × 5)

⇒ $9125 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9125 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9125 = P (1 + ²⁵/₁₀₀)

⇒ $9125 = P (^{100 + 25}/₁₀₀)

⇒ $9125 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9125

⇒ P = ⁹¹²⁵/_¹²⁵/100

⇒ P = 9125 × ¹⁰⁰/₁₂₅

⇒ P = ^{9125 × 100}/₁₂₅

⇒ P = ⁹¹²⁵⁰⁰/₁₂₅

⇒ P = $7300

Thus, the sum borrowed (P) = $7300 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 9125, then the Principal = ¹⁰⁰/₁₂₅ × 9125

= ^{100 × 9125}/₁₂₅

= ⁹¹²⁵⁰⁰/₁₂₅

= 7300

Thus, Principal = $7300

Thus, the sum borrowed = $7300 Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

(2) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(3) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

(4) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(8) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.

(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?

(10) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.