Simple Interest
Math MCQs

Question :    If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3672

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

$3672 = P (1 + 2% × 4)

⇒ $3672 = P (1 + ²/₁₀₀ × 4)

⇒ $3672 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3672 = P (1 + ⁸/₁₀₀)

⇒ $3672 = P (^{100 + 8}/₁₀₀)

⇒ $3672 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3672

⇒ P = ³⁶⁷²/_¹⁰⁸/100

⇒ P = 3672 × ¹⁰⁰/₁₀₈

⇒ P = ^{3672 × 100}/₁₀₈

⇒ P = ³⁶⁷²⁰⁰/₁₀₈

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 3672, then the Principal = ¹⁰⁰/₁₀₈ × 3672

= ^{100 × 3672}/₁₀₈

= ³⁶⁷²⁰⁰/₁₀₈

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.

(3) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.

(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?

(6) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

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

(8) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(10) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?