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) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(2) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.

(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(6) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(10) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?