Simple Interest
Math MCQs

Question :    Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3597

Rate of Simple Interest (R) = 3%

Time (T) = 3 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

$3597 = P (1 + 3% × 3)

⇒ $3597 = P (1 + ³/₁₀₀ × 3)

⇒ $3597 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3597 = P (1 + ⁹/₁₀₀)

⇒ $3597 = P (^{100 + 9}/₁₀₀)

⇒ $3597 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3597

⇒ P = ³⁵⁹⁷/_¹⁰⁹/100

⇒ P = 3597 × ¹⁰⁰/₁₀₉

⇒ P = ^{3597 × 100}/₁₀₉

⇒ P = ³⁵⁹⁷⁰⁰/₁₀₉

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3597, then the Principal = ¹⁰⁰/₁₀₉ × 3597

= ^{100 × 3597}/₁₀₉

= ³⁵⁹⁷⁰⁰/₁₀₉

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?

(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(6) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?

(9) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?