Simple Interest
Math MCQs

Question :  ( 1 of 10 )  If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4920

Rate of Simple Interest (R) = 5%

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

$4920 = P (1 + 5% × 4)

⇒ $4920 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4920 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4920 = P (1 + ²⁰/₁₀₀)

⇒ $4920 = P (^{100 + 20}/₁₀₀)

⇒ $4920 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4920

⇒ P = ⁴⁹²⁰/_¹²⁰/100

⇒ P = 4920 × ¹⁰⁰/₁₂₀

⇒ P = ^{4920 × 100}/₁₂₀

⇒ P = ⁴⁹²⁰⁰⁰/₁₂₀

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4920, then the Principal = ¹⁰⁰/₁₂₀ × 4920

= ^{100 × 4920}/₁₂₀

= ⁴⁹²⁰⁰⁰/₁₂₀

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

(2) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.

(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

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

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.

(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(8) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(9) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

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