Simple Interest
Math MCQs

Question :    How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?

Correct Answer  $6300

Solution & Explanation

Solution

Given,

Amount (A) = $7245

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

$7245 = P (1 + 3% × 5)

⇒ $7245 = P (1 + ³/₁₀₀ × 5)

⇒ $7245 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7245 = P (1 + ¹⁵/₁₀₀)

⇒ $7245 = P (^{100 + 15}/₁₀₀)

⇒ $7245 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7245

⇒ P = ⁷²⁴⁵/_¹¹⁵/100

⇒ P = 7245 × ¹⁰⁰/₁₁₅

⇒ P = ^{7245 × 100}/₁₁₅

⇒ P = ⁷²⁴⁵⁰⁰/₁₁₅

⇒ P = $6300

Thus, the sum borrowed (P) = $6300 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 7245, then the Principal = ¹⁰⁰/₁₁₅ × 7245

= ^{100 × 7245}/₁₁₅

= ⁷²⁴⁵⁰⁰/₁₁₅

= 6300

Thus, Principal = $6300

Thus, the sum borrowed = $6300 Answer

Similar Questions

(1) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.

(10) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.