Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $6622

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 = $6622 – $4300 = $2322

Thus, Simple Interest = $2322

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 × 2322}/_{4300 × 9}

= ²³²²⁰⁰/₃₈₇₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4300

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

Simple Interest = $2322 (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 $4300

= ⁹/₁₀₀ × 4300

= ^{9 × 4300}/₁₀₀

= ³⁸⁷⁰⁰/₁₀₀ = 387

Thus, simple Interest for 1 year = $387

Now,

∵ If the simple Interest is $387, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₇ years

∴ If the simple Interest is $2322, then the time = ¹/₃₈₇ × 2322 years

= ^{1 × 2322}/₃₈₇ years

= ²³²²/₃₈₇ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?

(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(4) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.

(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 8% simple interest?

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.