Simple Interest
Math MCQs

Question :    How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?

Correct Answer  $6600

Solution & Explanation

Solution

Given,

Amount (A) = $7260

Rate of Simple Interest (R) = 2%

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

$7260 = P (1 + 2% × 5)

⇒ $7260 = P (1 + ²/₁₀₀ × 5)

⇒ $7260 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7260 = P (1 + ¹⁰/₁₀₀)

⇒ $7260 = P (^{100 + 10}/₁₀₀)

⇒ $7260 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7260

⇒ P = ⁷²⁶⁰/_¹¹⁰/100

⇒ P = 7260 × ¹⁰⁰/₁₁₀

⇒ P = ^{7260 × 100}/₁₁₀

⇒ P = ⁷²⁶⁰⁰⁰/₁₁₀

⇒ P = $6600

Thus, the sum borrowed (P) = $6600 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7260, then the Principal = ¹⁰⁰/₁₁₀ × 7260

= ^{100 × 7260}/₁₁₀

= ⁷²⁶⁰⁰⁰/₁₁₀

= 6600

Thus, Principal = $6600

Thus, the sum borrowed = $6600 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(2) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?

(7) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.