Simple Interest
Math MCQs

Question :    How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Amount (A) = $7700

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

$7700 = P (1 + 2% × 5)

⇒ $7700 = P (1 + ²/₁₀₀ × 5)

⇒ $7700 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7700 = P (1 + ¹⁰/₁₀₀)

⇒ $7700 = P (^{100 + 10}/₁₀₀)

⇒ $7700 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7700

⇒ P = ⁷⁷⁰⁰/_¹¹⁰/100

⇒ P = 7700 × ¹⁰⁰/₁₁₀

⇒ P = ^{7700 × 100}/₁₁₀

⇒ P = ⁷⁷⁰⁰⁰⁰/₁₁₀

⇒ P = $7000

Thus, the sum borrowed (P) = $7000 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 7700, then the Principal = ¹⁰⁰/₁₁₀ × 7700

= ^{100 × 7700}/₁₁₀

= ⁷⁷⁰⁰⁰⁰/₁₁₀

= 7000

Thus, Principal = $7000

Thus, the sum borrowed = $7000 Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.

(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(6) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(8) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.