Simple Interest
Math MCQs

Question :    How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?

Correct Answer  $6600

Solution & Explanation

Solution

Given,

Amount (A) = $7590

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

$7590 = P (1 + 3% × 5)

⇒ $7590 = P (1 + ³/₁₀₀ × 5)

⇒ $7590 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7590 = P (1 + ¹⁵/₁₀₀)

⇒ $7590 = P (^{100 + 15}/₁₀₀)

⇒ $7590 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7590

⇒ P = ⁷⁵⁹⁰/_¹¹⁵/100

⇒ P = 7590 × ¹⁰⁰/₁₁₅

⇒ P = ^{7590 × 100}/₁₁₅

⇒ P = ⁷⁵⁹⁰⁰⁰/₁₁₅

⇒ P = $6600

Thus, the sum borrowed (P) = $6600 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 7590, then the Principal = ¹⁰⁰/₁₁₅ × 7590

= ^{100 × 7590}/₁₁₅

= ⁷⁵⁹⁰⁰⁰/₁₁₅

= 6600

Thus, Principal = $6600

Thus, the sum borrowed = $6600 Answer

Similar Questions

(1) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(3) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.

(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.

(9) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.