Simple Interest
Math MCQs

Question :    How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

Correct Answer  $5800

Solution & Explanation

Solution

Given,

Amount (A) = $6960

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

$6960 = P (1 + 4% × 5)

⇒ $6960 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6960 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6960 = P (1 + ²⁰/₁₀₀)

⇒ $6960 = P (^{100 + 20}/₁₀₀)

⇒ $6960 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6960

⇒ P = ⁶⁹⁶⁰/_¹²⁰/100

⇒ P = 6960 × ¹⁰⁰/₁₂₀

⇒ P = ^{6960 × 100}/₁₂₀

⇒ P = ⁶⁹⁶⁰⁰⁰/₁₂₀

⇒ P = $5800

Thus, the sum borrowed (P) = $5800 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 6960, then the Principal = ¹⁰⁰/₁₂₀ × 6960

= ^{100 × 6960}/₁₂₀

= ⁶⁹⁶⁰⁰⁰/₁₂₀

= 5800

Thus, Principal = $5800

Thus, the sum borrowed = $5800 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.

(6) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.