Simple Interest
Math MCQs

Question :    How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

Correct Answer  $7400

Solution & Explanation

Solution

Given,

Amount (A) = $9250

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

$9250 = P (1 + 5% × 5)

⇒ $9250 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9250 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9250 = P (1 + ²⁵/₁₀₀)

⇒ $9250 = P (^{100 + 25}/₁₀₀)

⇒ $9250 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9250

⇒ P = ⁹²⁵⁰/_¹²⁵/100

⇒ P = 9250 × ¹⁰⁰/₁₂₅

⇒ P = ^{9250 × 100}/₁₂₅

⇒ P = ⁹²⁵⁰⁰⁰/₁₂₅

⇒ P = $7400

Thus, the sum borrowed (P) = $7400 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 9250, then the Principal = ¹⁰⁰/₁₂₅ × 9250

= ^{100 × 9250}/₁₂₅

= ⁹²⁵⁰⁰⁰/₁₂₅

= 7400

Thus, Principal = $7400

Thus, the sum borrowed = $7400 Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?

(3) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.

(7) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(10) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.