Simple Interest
Math MCQs

Question :    If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3510

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

$3510 = P (1 + 2% × 4)

⇒ $3510 = P (1 + ²/₁₀₀ × 4)

⇒ $3510 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3510 = P (1 + ⁸/₁₀₀)

⇒ $3510 = P (^{100 + 8}/₁₀₀)

⇒ $3510 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3510

⇒ P = ³⁵¹⁰/_¹⁰⁸/100

⇒ P = 3510 × ¹⁰⁰/₁₀₈

⇒ P = ^{3510 × 100}/₁₀₈

⇒ P = ³⁵¹⁰⁰⁰/₁₀₈

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 3510, then the Principal = ¹⁰⁰/₁₀₈ × 3510

= ^{100 × 3510}/₁₀₈

= ³⁵¹⁰⁰⁰/₁₀₈

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.

(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

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

(8) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?

(10) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.