Simple Interest
Math MCQs

Question :    If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3618

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

$3618 = P (1 + 2% × 4)

⇒ $3618 = P (1 + ²/₁₀₀ × 4)

⇒ $3618 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3618 = P (1 + ⁸/₁₀₀)

⇒ $3618 = P (^{100 + 8}/₁₀₀)

⇒ $3618 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3618

⇒ P = ³⁶¹⁸/_¹⁰⁸/100

⇒ P = 3618 × ¹⁰⁰/₁₀₈

⇒ P = ^{3618 × 100}/₁₀₈

⇒ P = ³⁶¹⁸⁰⁰/₁₀₈

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3618, then the Principal = ¹⁰⁰/₁₀₈ × 3618

= ^{100 × 3618}/₁₀₈

= ³⁶¹⁸⁰⁰/₁₀₈

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

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

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?

(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(5) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?

(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

(8) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(9) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 4% simple interest?