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) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?

(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?

(3) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?

(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.