Simple Interest
Math MCQs

Question :    If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4680

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

$4680 = P (1 + 5% × 4)

⇒ $4680 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4680 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4680 = P (1 + ²⁰/₁₀₀)

⇒ $4680 = P (^{100 + 20}/₁₀₀)

⇒ $4680 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4680

⇒ P = ⁴⁶⁸⁰/_¹²⁰/100

⇒ P = 4680 × ¹⁰⁰/₁₂₀

⇒ P = ^{4680 × 100}/₁₂₀

⇒ P = ⁴⁶⁸⁰⁰⁰/₁₂₀

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4680, then the Principal = ¹⁰⁰/₁₂₀ × 4680

= ^{100 × 4680}/₁₂₀

= ⁴⁶⁸⁰⁰⁰/₁₂₀

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(2) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(3) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?

(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?

(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?

(10) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.