Simple Interest
Math MCQs

Question :    How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

Correct Answer  $6500

Solution & Explanation

Solution

Given,

Amount (A) = $7475

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

$7475 = P (1 + 3% × 5)

⇒ $7475 = P (1 + ³/₁₀₀ × 5)

⇒ $7475 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7475 = P (1 + ¹⁵/₁₀₀)

⇒ $7475 = P (^{100 + 15}/₁₀₀)

⇒ $7475 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7475

⇒ P = ⁷⁴⁷⁵/_¹¹⁵/100

⇒ P = 7475 × ¹⁰⁰/₁₁₅

⇒ P = ^{7475 × 100}/₁₁₅

⇒ P = ⁷⁴⁷⁵⁰⁰/₁₁₅

⇒ P = $6500

Thus, the sum borrowed (P) = $6500 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 7475, then the Principal = ¹⁰⁰/₁₁₅ × 7475

= ^{100 × 7475}/₁₁₅

= ⁷⁴⁷⁵⁰⁰/₁₁₅

= 6500

Thus, Principal = $6500

Thus, the sum borrowed = $6500 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.

(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.

(6) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.

(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?

(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(9) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.

(10) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.