Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9690

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9690 – $5100 = $4590

Thus, Simple Interest = $4590

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4590}/_{5100 × 9}

= ⁴⁵⁹⁰⁰⁰/₄₅₉₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $5100

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4590 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $5100

= ⁹/₁₀₀ × 5100

= ^{9 × 5100}/₁₀₀

= ⁴⁵⁹⁰⁰/₁₀₀ = 459

Thus, simple Interest for 1 year = $459

Now,

∵ If the simple Interest is $459, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₉ years

∴ If the simple Interest is $4590, then the time = ¹/₄₅₉ × 4590 years

= ^{1 × 4590}/₄₅₉ years

= ⁴⁵⁹⁰/₄₅₉ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?

(2) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.

(10) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?