Simple Interest
Math MCQs

Question :    How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?

Correct Answer  $6950

Solution & Explanation

Solution

Given,

Amount (A) = $8340

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

$8340 = P (1 + 4% × 5)

⇒ $8340 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8340 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8340 = P (1 + ²⁰/₁₀₀)

⇒ $8340 = P (^{100 + 20}/₁₀₀)

⇒ $8340 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8340

⇒ P = ⁸³⁴⁰/_¹²⁰/100

⇒ P = 8340 × ¹⁰⁰/₁₂₀

⇒ P = ^{8340 × 100}/₁₂₀

⇒ P = ⁸³⁴⁰⁰⁰/₁₂₀

⇒ P = $6950

Thus, the sum borrowed (P) = $6950 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 8340, then the Principal = ¹⁰⁰/₁₂₀ × 8340

= ^{100 × 8340}/₁₂₀

= ⁸³⁴⁰⁰⁰/₁₂₀

= 6950

Thus, Principal = $6950

Thus, the sum borrowed = $6950 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.

(4) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.

(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.