Simple Interest
Math MCQs

Question :    How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

Correct Answer  $6450

Solution & Explanation

Solution

Given,

Amount (A) = $7740

Rate of Simple Interest (R) = 4%

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

$7740 = P (1 + 4% × 5)

⇒ $7740 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7740 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7740 = P (1 + ²⁰/₁₀₀)

⇒ $7740 = P (^{100 + 20}/₁₀₀)

⇒ $7740 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7740

⇒ P = ⁷⁷⁴⁰/_¹²⁰/100

⇒ P = 7740 × ¹⁰⁰/₁₂₀

⇒ P = ^{7740 × 100}/₁₂₀

⇒ P = ⁷⁷⁴⁰⁰⁰/₁₂₀

⇒ P = $6450

Thus, the sum borrowed (P) = $6450 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7740, then the Principal = ¹⁰⁰/₁₂₀ × 7740

= ^{100 × 7740}/₁₂₀

= ⁷⁷⁴⁰⁰⁰/₁₂₀

= 6450

Thus, Principal = $6450

Thus, the sum borrowed = $6450 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?

(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?

(5) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(6) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.

(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.

(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(9) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.