Simple Interest
Math MCQs

Question :    If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4144

Rate of Simple Interest (R) = 3%

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

$4144 = P (1 + 3% × 4)

⇒ $4144 = P (1 + ³/₁₀₀ × 4)

⇒ $4144 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4144 = P (1 + ¹²/₁₀₀)

⇒ $4144 = P (^{100 + 12}/₁₀₀)

⇒ $4144 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4144

⇒ P = ⁴¹⁴⁴/_¹¹²/100

⇒ P = 4144 × ¹⁰⁰/₁₁₂

⇒ P = ^{4144 × 100}/₁₁₂

⇒ P = ⁴¹⁴⁴⁰⁰/₁₁₂

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 = 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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4144, then the Principal = ¹⁰⁰/₁₁₂ × 4144

= ^{100 × 4144}/₁₁₂

= ⁴¹⁴⁴⁰⁰/₁₁₂

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?

(2) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?

(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

(7) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.

(9) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(10) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.