Simple Interest
Math MCQs

Question :    How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

Correct Answer  $7350

Solution & Explanation

Solution

Given,

Amount (A) = $8452.5

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

$8452.5 = P (1 + 3% × 5)

⇒ $8452.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8452.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8452.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8452.5 = P (^{100 + 15}/₁₀₀)

⇒ $8452.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8452.5

⇒ P = ^8452.5/_¹¹⁵/100

⇒ P = 8452.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8452.5 × 100}/₁₁₅

⇒ P = ⁸⁴⁵²⁵⁰/₁₁₅

⇒ P = $7350

Thus, the sum borrowed (P) = $7350 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 8452.5, then the Principal = ¹⁰⁰/₁₁₅ × 8452.5

= ^{100 × 8452.5}/₁₁₅

= ⁸⁴⁵²⁵⁰/₁₁₅

= 7350

Thus, Principal = $7350

Thus, the sum borrowed = $7350 Answer

Similar Questions

(1) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

(4) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?

(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(10) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?