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) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.

(6) How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(8) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.