Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $11780

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 = $11780 – $6200 = $5580

Thus, Simple Interest = $5580

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 × 5580}/_{6200 × 9}

= ⁵⁵⁸⁰⁰⁰/₅₅₈₀₀

= 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) = $6200

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

Simple Interest = $5580 (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 $6200

= ⁹/₁₀₀ × 6200

= ^{9 × 6200}/₁₀₀

= ⁵⁵⁸⁰⁰/₁₀₀ = 558

Thus, simple Interest for 1 year = $558

Now,

∵ If the simple Interest is $558, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₈ years

∴ If the simple Interest is $5580, then the time = ¹/₅₅₈ × 5580 years

= ^{1 × 5580}/₅₅₈ years

= ⁵⁵⁸⁰/₅₅₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?

(2) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(4) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?