Simple Interest
Math MCQs

Question :    How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

Correct Answer  $5050

Solution & Explanation

Solution

Given,

Amount (A) = $6312.5

Rate of Simple Interest (R) = 5%

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

$6312.5 = P (1 + 5% × 5)

⇒ $6312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6312.5 = P (1 + ²⁵/₁₀₀)

⇒ $6312.5 = P (^{100 + 25}/₁₀₀)

⇒ $6312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6312.5

⇒ P = ^6312.5/_¹²⁵/100

⇒ P = 6312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6312.5 × 100}/₁₂₅

⇒ P = ⁶³¹²⁵⁰/₁₂₅

⇒ P = $5050

Thus, the sum borrowed (P) = $5050 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6312.5, then the Principal = ¹⁰⁰/₁₂₅ × 6312.5

= ^{100 × 6312.5}/₁₂₅

= ⁶³¹²⁵⁰/₁₂₅

= 5050

Thus, Principal = $5050

Thus, the sum borrowed = $5050 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) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

(6) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.

(8) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

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

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