Simple Interest
Math MCQs

Question :    If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5076

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$5076 = P (1 + 2% × 4)

⇒ $5076 = P (1 + ²/₁₀₀ × 4)

⇒ $5076 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5076 = P (1 + ⁸/₁₀₀)

⇒ $5076 = P (^{100 + 8}/₁₀₀)

⇒ $5076 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5076

⇒ P = ⁵⁰⁷⁶/_¹⁰⁸/100

⇒ P = 5076 × ¹⁰⁰/₁₀₈

⇒ P = ^{5076 × 100}/₁₀₈

⇒ P = ⁵⁰⁷⁶⁰⁰/₁₀₈

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 5076, then the Principal = ¹⁰⁰/₁₀₈ × 5076

= ^{100 × 5076}/₁₀₈

= ⁵⁰⁷⁶⁰⁰/₁₀₈

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(3) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.

(4) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(6) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

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

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.

(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.

(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?