Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $8940

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$8940 = P (1 + 4% × 5)

⇒ $8940 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8940 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8940 = P (1 + ²⁰/₁₀₀)

⇒ $8940 = P (^{100 + 20}/₁₀₀)

⇒ $8940 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8940

⇒ P = ⁸⁹⁴⁰/_¹²⁰/100

⇒ P = 8940 × ¹⁰⁰/₁₂₀

⇒ P = ^{8940 × 100}/₁₂₀

⇒ P = ⁸⁹⁴⁰⁰⁰/₁₂₀

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8940, then the Principal = ¹⁰⁰/₁₂₀ × 8940

= ^{100 × 8940}/₁₂₀

= ⁸⁹⁴⁰⁰⁰/₁₂₀

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(3) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

(4) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.

(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.

(10) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.