Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $9540

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

$9540 = P (1 + 4% × 5)

⇒ $9540 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9540 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9540 = P (1 + ²⁰/₁₀₀)

⇒ $9540 = P (^{100 + 20}/₁₀₀)

⇒ $9540 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9540

⇒ P = ⁹⁵⁴⁰/_¹²⁰/100

⇒ P = 9540 × ¹⁰⁰/₁₂₀

⇒ P = ^{9540 × 100}/₁₂₀

⇒ P = ⁹⁵⁴⁰⁰⁰/₁₂₀

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 9540, then the Principal = ¹⁰⁰/₁₂₀ × 9540

= ^{100 × 9540}/₁₂₀

= ⁹⁵⁴⁰⁰⁰/₁₂₀

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(3) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(7) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

(9) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.