Simple Interest
Math MCQs

Question :    How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?

Correct Answer  $6950

Solution & Explanation

Solution

Given,

Amount (A) = $7992.5

Rate of Simple Interest (R) = 3%

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

$7992.5 = P (1 + 3% × 5)

⇒ $7992.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7992.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7992.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7992.5 = P (^{100 + 15}/₁₀₀)

⇒ $7992.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7992.5

⇒ P = ^7992.5/_¹¹⁵/100

⇒ P = 7992.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7992.5 × 100}/₁₁₅

⇒ P = ⁷⁹⁹²⁵⁰/₁₁₅

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7992.5, then the Principal = ¹⁰⁰/₁₁₅ × 7992.5

= ^{100 × 7992.5}/₁₁₅

= ⁷⁹⁹²⁵⁰/₁₁₅

= 6950

Thus, Principal = $6950

Thus, the sum borrowed = $6950 Answer

Similar Questions

(1) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.

(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?

(5) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?

(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?

(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(10) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.