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) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?

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

(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(5) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 6% simple interest?

(10) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.