Simple Interest
Math MCQs

Question :    If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3640

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

$3640 = P (1 + 3% × 4)

⇒ $3640 = P (1 + ³/₁₀₀ × 4)

⇒ $3640 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3640 = P (1 + ¹²/₁₀₀)

⇒ $3640 = P (^{100 + 12}/₁₀₀)

⇒ $3640 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3640

⇒ P = ³⁶⁴⁰/_¹¹²/100

⇒ P = 3640 × ¹⁰⁰/₁₁₂

⇒ P = ^{3640 × 100}/₁₁₂

⇒ P = ³⁶⁴⁰⁰⁰/₁₁₂

⇒ 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 = 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 3640, then the Principal = ¹⁰⁰/₁₁₂ × 3640

= ^{100 × 3640}/₁₁₂

= ³⁶⁴⁰⁰⁰/₁₁₂

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.

(2) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?

(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(6) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.

(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(10) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.