Simple Interest
Math MCQs

Question :    If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4482

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

$4482 = P (1 + 2% × 4)

⇒ $4482 = P (1 + ²/₁₀₀ × 4)

⇒ $4482 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4482 = P (1 + ⁸/₁₀₀)

⇒ $4482 = P (^{100 + 8}/₁₀₀)

⇒ $4482 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4482

⇒ P = ⁴⁴⁸²/_¹⁰⁸/100

⇒ P = 4482 × ¹⁰⁰/₁₀₈

⇒ P = ^{4482 × 100}/₁₀₈

⇒ P = ⁴⁴⁸²⁰⁰/₁₀₈

⇒ P = $4150

Thus, the sum borrowed (P) = $4150 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 4482, then the Principal = ¹⁰⁰/₁₀₈ × 4482

= ^{100 × 4482}/₁₀₈

= ⁴⁴⁸²⁰⁰/₁₀₈

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(6) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.