Simple Interest
Math MCQs

Question :  ( 1 of 10 )  Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7310

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 = $7310 – $4300 = $3010

Thus, Simple Interest = $3010

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 × 3010}/_{4300 × 7}

= ³⁰¹⁰⁰⁰/₃₀₁₀₀

= 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) = $4300

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3010 (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 = 7% of Principal

= 7% of $4300

= ⁷/₁₀₀ × 4300

= ^{7 × 4300}/₁₀₀

= ³⁰¹⁰⁰/₁₀₀ = 301

Thus, simple Interest for 1 year = $301

Now,

∵ If the simple Interest is $301, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₁ years

∴ If the simple Interest is $3010, then the time = ¹/₃₀₁ × 3010 years

= ^{1 × 3010}/₃₀₁ years

= ³⁰¹⁰/₃₀₁ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.

(2) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(3) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?

(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

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

(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(10) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?