Simple Interest
Math MCQs

Question :    If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3770

Rate of Simple Interest (R) = 4%

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

$3770 = P (1 + 4% × 4)

⇒ $3770 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3770 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3770 = P (1 + ¹⁶/₁₀₀)

⇒ $3770 = P (^{100 + 16}/₁₀₀)

⇒ $3770 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3770

⇒ P = ³⁷⁷⁰/_¹¹⁶/100

⇒ P = 3770 × ¹⁰⁰/₁₁₆

⇒ P = ^{3770 × 100}/₁₁₆

⇒ P = ³⁷⁷⁰⁰⁰/₁₁₆

⇒ 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 = 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3770, then the Principal = ¹⁰⁰/₁₁₆ × 3770

= ^{100 × 3770}/₁₁₆

= ³⁷⁷⁰⁰⁰/₁₁₆

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(3) How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?

(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(5) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

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

(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(8) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.

(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?

(10) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.