Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6382.5

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

$6382.5 = P (1 + 3% × 5)

⇒ $6382.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6382.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6382.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6382.5 = P (^{100 + 15}/₁₀₀)

⇒ $6382.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6382.5

⇒ P = ^6382.5/_¹¹⁵/100

⇒ P = 6382.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6382.5 × 100}/₁₁₅

⇒ P = ⁶³⁸²⁵⁰/₁₁₅

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 6382.5, then the Principal = ¹⁰⁰/₁₁₅ × 6382.5

= ^{100 × 6382.5}/₁₁₅

= ⁶³⁸²⁵⁰/₁₁₅

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(3) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.

(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.

(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.