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) 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?

(2) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(4) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?

(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(6) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(9) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?