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) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?

(6) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.

(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(9) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?