Simple Interest
Math MCQs

Question :    How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $5865

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

$5865 = P (1 + 3% × 5)

⇒ $5865 = P (1 + ³/₁₀₀ × 5)

⇒ $5865 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $5865 = P (1 + ¹⁵/₁₀₀)

⇒ $5865 = P (^{100 + 15}/₁₀₀)

⇒ $5865 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5865

⇒ P = ⁵⁸⁶⁵/_¹¹⁵/100

⇒ P = 5865 × ¹⁰⁰/₁₁₅

⇒ P = ^{5865 × 100}/₁₁₅

⇒ P = ⁵⁸⁶⁵⁰⁰/₁₁₅

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 5865, then the Principal = ¹⁰⁰/₁₁₅ × 5865

= ^{100 × 5865}/₁₁₅

= ⁵⁸⁶⁵⁰⁰/₁₁₅

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?

(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(4) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?

(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(7) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.