Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $10148

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 = $10148 – $5900 = $4248

Thus, Simple Interest = $4248

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 × 4248}/_{5900 × 9}

= ⁴²⁴⁸⁰⁰/₅₃₁₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5900

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

Simple Interest = $4248 (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 $5900

= ⁹/₁₀₀ × 5900

= ^{9 × 5900}/₁₀₀

= ⁵³¹⁰⁰/₁₀₀ = 531

Thus, simple Interest for 1 year = $531

Now,

∵ If the simple Interest is $531, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₁ years

∴ If the simple Interest is $4248, then the time = ¹/₅₃₁ × 4248 years

= ^{1 × 4248}/₅₃₁ years

= ⁴²⁴⁸/₅₃₁ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

(3) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(5) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.