Simple Interest
Math MCQs

Question :    How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5500

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

$5500 = P (1 + 2% × 5)

⇒ $5500 = P (1 + ²/₁₀₀ × 5)

⇒ $5500 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5500 = P (1 + ¹⁰/₁₀₀)

⇒ $5500 = P (^{100 + 10}/₁₀₀)

⇒ $5500 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5500

⇒ P = ⁵⁵⁰⁰/_¹¹⁰/100

⇒ P = 5500 × ¹⁰⁰/₁₁₀

⇒ P = ^{5500 × 100}/₁₁₀

⇒ P = ⁵⁵⁰⁰⁰⁰/₁₁₀

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5500, then the Principal = ¹⁰⁰/₁₁₀ × 5500

= ^{100 × 5500}/₁₁₀

= ⁵⁵⁰⁰⁰⁰/₁₁₀

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(2) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.

(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(6) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?