Simple Interest
Math MCQs

Question :    How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?

Correct Answer  $7700

Solution & Explanation

Solution

Given,

Amount (A) = $9240

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

$9240 = P (1 + 4% × 5)

⇒ $9240 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9240 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9240 = P (1 + ²⁰/₁₀₀)

⇒ $9240 = P (^{100 + 20}/₁₀₀)

⇒ $9240 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9240

⇒ P = ⁹²⁴⁰/_¹²⁰/100

⇒ P = 9240 × ¹⁰⁰/₁₂₀

⇒ P = ^{9240 × 100}/₁₂₀

⇒ P = ⁹²⁴⁰⁰⁰/₁₂₀

⇒ P = $7700

Thus, the sum borrowed (P) = $7700 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 9240, then the Principal = ¹⁰⁰/₁₂₀ × 9240

= ^{100 × 9240}/₁₂₀

= ⁹²⁴⁰⁰⁰/₁₂₀

= 7700

Thus, Principal = $7700

Thus, the sum borrowed = $7700 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(4) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.

(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?

(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.