Simple Interest
Math MCQs

Question :    If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3294

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

$3294 = P (1 + 2% × 4)

⇒ $3294 = P (1 + ²/₁₀₀ × 4)

⇒ $3294 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3294 = P (1 + ⁸/₁₀₀)

⇒ $3294 = P (^{100 + 8}/₁₀₀)

⇒ $3294 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3294

⇒ P = ³²⁹⁴/_¹⁰⁸/100

⇒ P = 3294 × ¹⁰⁰/₁₀₈

⇒ P = ^{3294 × 100}/₁₀₈

⇒ P = ³²⁹⁴⁰⁰/₁₀₈

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 3294, then the Principal = ¹⁰⁰/₁₀₈ × 3294

= ^{100 × 3294}/₁₀₈

= ³²⁹⁴⁰⁰/₁₀₈

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.

(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

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

(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.

(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.