Simple Interest
Math MCQs

Question :    If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5346

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

$5346 = P (1 + 2% × 4)

⇒ $5346 = P (1 + ²/₁₀₀ × 4)

⇒ $5346 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5346 = P (1 + ⁸/₁₀₀)

⇒ $5346 = P (^{100 + 8}/₁₀₀)

⇒ $5346 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5346

⇒ P = ⁵³⁴⁶/_¹⁰⁸/100

⇒ P = 5346 × ¹⁰⁰/₁₀₈

⇒ P = ^{5346 × 100}/₁₀₈

⇒ P = ⁵³⁴⁶⁰⁰/₁₀₈

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 5346, then the Principal = ¹⁰⁰/₁₀₈ × 5346

= ^{100 × 5346}/₁₀₈

= ⁵³⁴⁶⁰⁰/₁₀₈

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.

(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(3) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(6) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.

(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.