Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $9120

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

$9120 = P (1 + 4% × 5)

⇒ $9120 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9120 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9120 = P (1 + ²⁰/₁₀₀)

⇒ $9120 = P (^{100 + 20}/₁₀₀)

⇒ $9120 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9120

⇒ P = ⁹¹²⁰/_¹²⁰/100

⇒ P = 9120 × ¹⁰⁰/₁₂₀

⇒ P = ^{9120 × 100}/₁₂₀

⇒ P = ⁹¹²⁰⁰⁰/₁₂₀

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 9120, then the Principal = ¹⁰⁰/₁₂₀ × 9120

= ^{100 × 9120}/₁₂₀

= ⁹¹²⁰⁰⁰/₁₂₀

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.

(5) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.

(7) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.

(9) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?