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) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

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

(5) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.

(7) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?

(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?

(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?