Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $6152.5

Rate of Simple Interest (R) = 3%

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

$6152.5 = P (1 + 3% × 5)

⇒ $6152.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6152.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6152.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6152.5 = P (^{100 + 15}/₁₀₀)

⇒ $6152.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6152.5

⇒ P = ^6152.5/_¹¹⁵/100

⇒ P = 6152.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6152.5 × 100}/₁₁₅

⇒ P = ⁶¹⁵²⁵⁰/₁₁₅

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6152.5, then the Principal = ¹⁰⁰/₁₁₅ × 6152.5

= ^{100 × 6152.5}/₁₁₅

= ⁶¹⁵²⁵⁰/₁₁₅

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?

(2) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.

(5) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.

(8) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.

(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?