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) 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.

(2) 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.

(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?