Simple Interest
Math MCQs

Question :    If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5432

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

$5432 = P (1 + 3% × 4)

⇒ $5432 = P (1 + ³/₁₀₀ × 4)

⇒ $5432 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5432 = P (1 + ¹²/₁₀₀)

⇒ $5432 = P (^{100 + 12}/₁₀₀)

⇒ $5432 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5432

⇒ P = ⁵⁴³²/_¹¹²/100

⇒ P = 5432 × ¹⁰⁰/₁₁₂

⇒ P = ^{5432 × 100}/₁₁₂

⇒ P = ⁵⁴³²⁰⁰/₁₁₂

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5432, then the Principal = ¹⁰⁰/₁₁₂ × 5432

= ^{100 × 5432}/₁₁₂

= ⁵⁴³²⁰⁰/₁₁₂

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

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

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(4) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

(10) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.