Simple Interest
Math MCQs

Question :    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?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $9420

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

$9420 = P (1 + 4% × 5)

⇒ $9420 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9420 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9420 = P (1 + ²⁰/₁₀₀)

⇒ $9420 = P (^{100 + 20}/₁₀₀)

⇒ $9420 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9420

⇒ P = ⁹⁴²⁰/_¹²⁰/100

⇒ P = 9420 × ¹⁰⁰/₁₂₀

⇒ P = ^{9420 × 100}/₁₂₀

⇒ P = ⁹⁴²⁰⁰⁰/₁₂₀

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 9420, then the Principal = ¹⁰⁰/₁₂₀ × 9420

= ^{100 × 9420}/₁₂₀

= ⁹⁴²⁰⁰⁰/₁₂₀

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?

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

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(6) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.

(8) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.