Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4408

Rate of Simple Interest (R) = 4%

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

$4408 = P (1 + 4% × 4)

⇒ $4408 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4408 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4408 = P (1 + ¹⁶/₁₀₀)

⇒ $4408 = P (^{100 + 16}/₁₀₀)

⇒ $4408 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4408

⇒ P = ⁴⁴⁰⁸/_¹¹⁶/100

⇒ P = 4408 × ¹⁰⁰/₁₁₆

⇒ P = ^{4408 × 100}/₁₁₆

⇒ P = ⁴⁴⁰⁸⁰⁰/₁₁₆

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4408, then the Principal = ¹⁰⁰/₁₁₆ × 4408

= ^{100 × 4408}/₁₁₆

= ⁴⁴⁰⁸⁰⁰/₁₁₆

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.

(3) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.