Simple Interest
Math MCQs

Question :    If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3564

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$3564 = P (1 + 2% × 4)

⇒ $3564 = P (1 + ²/₁₀₀ × 4)

⇒ $3564 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3564 = P (1 + ⁸/₁₀₀)

⇒ $3564 = P (^{100 + 8}/₁₀₀)

⇒ $3564 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3564

⇒ P = ³⁵⁶⁴/_¹⁰⁸/100

⇒ P = 3564 × ¹⁰⁰/₁₀₈

⇒ P = ^{3564 × 100}/₁₀₈

⇒ P = ³⁵⁶⁴⁰⁰/₁₀₈

⇒ 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 = 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 3564, then the Principal = ¹⁰⁰/₁₀₈ × 3564

= ^{100 × 3564}/₁₀₈

= ³⁵⁶⁴⁰⁰/₁₀₈

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(2) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(4) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(6) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?

(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(9) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.