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) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?

(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(4) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?

(8) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?