Simple Interest
Math MCQs

Question :    If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3900

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

$3900 = P (1 + 5% × 4)

⇒ $3900 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3900 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3900 = P (1 + ²⁰/₁₀₀)

⇒ $3900 = P (^{100 + 20}/₁₀₀)

⇒ $3900 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3900

⇒ P = ³⁹⁰⁰/_¹²⁰/100

⇒ P = 3900 × ¹⁰⁰/₁₂₀

⇒ P = ^{3900 × 100}/₁₂₀

⇒ P = ³⁹⁰⁰⁰⁰/₁₂₀

⇒ 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 = 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 3900, then the Principal = ¹⁰⁰/₁₂₀ × 3900

= ^{100 × 3900}/₁₂₀

= ³⁹⁰⁰⁰⁰/₁₂₀

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.

(7) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?

(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.