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) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(4) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.

(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?

(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(10) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?