Simple Interest
Math MCQs

Question :    How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

Correct Answer  $6200

Solution & Explanation

Solution

Given,

Amount (A) = $7750

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

$7750 = P (1 + 5% × 5)

⇒ $7750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7750 = P (1 + ²⁵/₁₀₀)

⇒ $7750 = P (^{100 + 25}/₁₀₀)

⇒ $7750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7750

⇒ P = ⁷⁷⁵⁰/_¹²⁵/100

⇒ P = 7750 × ¹⁰⁰/₁₂₅

⇒ P = ^{7750 × 100}/₁₂₅

⇒ P = ⁷⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $6200

Thus, the sum borrowed (P) = $6200 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 7750, then the Principal = ¹⁰⁰/₁₂₅ × 7750

= ^{100 × 7750}/₁₂₅

= ⁷⁷⁵⁰⁰⁰/₁₂₅

= 6200

Thus, Principal = $6200

Thus, the sum borrowed = $6200 Answer

Similar Questions

(1) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(6) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(8) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(9) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.