Simple Interest
Math MCQs

Question :    How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $8250

Rate of Simple Interest (R) = 2%

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

$8250 = P (1 + 2% × 5)

⇒ $8250 = P (1 + ²/₁₀₀ × 5)

⇒ $8250 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8250 = P (1 + ¹⁰/₁₀₀)

⇒ $8250 = P (^{100 + 10}/₁₀₀)

⇒ $8250 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8250

⇒ P = ⁸²⁵⁰/_¹¹⁰/100

⇒ P = 8250 × ¹⁰⁰/₁₁₀

⇒ P = ^{8250 × 100}/₁₁₀

⇒ P = ⁸²⁵⁰⁰⁰/₁₁₀

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8250, then the Principal = ¹⁰⁰/₁₁₀ × 8250

= ^{100 × 8250}/₁₁₀

= ⁸²⁵⁰⁰⁰/₁₁₀

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(2) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 3% simple interest?

(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(6) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?

(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.