Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $4025

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4025 = P (1 + 5% × 3)

⇒ $4025 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4025 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4025 = P (1 + ¹⁵/₁₀₀)

⇒ $4025 = P (^{100 + 15}/₁₀₀)

⇒ $4025 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4025

⇒ P = ⁴⁰²⁵/_¹¹⁵/100

⇒ P = 4025 × ¹⁰⁰/₁₁₅

⇒ P = ^{4025 × 100}/₁₁₅

⇒ P = ⁴⁰²⁵⁰⁰/₁₁₅

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 4025, then the Principal = ¹⁰⁰/₁₁₅ × 4025

= ^{100 × 4025}/₁₁₅

= ⁴⁰²⁵⁰⁰/₁₁₅

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?

(2) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(5) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

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

(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.

(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?

(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?