Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 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) = 8% per annum

Amount (A) = $9676

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 = $9676 – $5900 = $3776

Thus, Simple Interest = $3776

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 × 3776}/_{5900 × 8}

= ³⁷⁷⁶⁰⁰/₄₇₂₀₀

= 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) = 8% per annum

Simple Interest = $3776 (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 = 8% of Principal

= 8% of $5900

= ⁸/₁₀₀ × 5900

= ^{8 × 5900}/₁₀₀

= ⁴⁷²⁰⁰/₁₀₀ = 472

Thus, simple Interest for 1 year = $472

Now,

∵ If the simple Interest is $472, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₂ years

∴ If the simple Interest is $3776, then the time = ¹/₄₇₂ × 3776 years

= ^{1 × 3776}/₄₇₂ years

= ³⁷⁷⁶/₄₇₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?

(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(5) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(6) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

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