Simple Interest
Math MCQs

Question :    Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4816

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$4816 = P (1 + 4% × 3)

⇒ $4816 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4816 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4816 = P (1 + ¹²/₁₀₀)

⇒ $4816 = P (^{100 + 12}/₁₀₀)

⇒ $4816 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4816

⇒ P = ⁴⁸¹⁶/_¹¹²/100

⇒ P = 4816 × ¹⁰⁰/₁₁₂

⇒ P = ^{4816 × 100}/₁₁₂

⇒ P = ⁴⁸¹⁶⁰⁰/₁₁₂

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 4816, then the Principal = ¹⁰⁰/₁₁₂ × 4816

= ^{100 × 4816}/₁₁₂

= ⁴⁸¹⁶⁰⁰/₁₁₂

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(2) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(3) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?

(5) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.

(7) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

(10) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?