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) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 7 years.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 8% simple interest?

(4) Betty had to pay $4632.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

(7) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?

(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?

(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?