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) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?

(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?

(5) 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.

(6) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?

(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

(10) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?