Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4300

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6106

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 = $6106 – $4300 = $1806

Thus, Simple Interest = $1806

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 × 1806}/_{4300 × 6}

= ¹⁸⁰⁶⁰⁰/₂₅₈₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 6% per annum

Simple Interest = $1806 (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 = 6% of Principal

= 6% of $4300

= ⁶/₁₀₀ × 4300

= ^{6 × 4300}/₁₀₀

= ²⁵⁸⁰⁰/₁₀₀ = 258

Thus, simple Interest for 1 year = $258

Now,

∵ If the simple Interest is $258, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₅₈ years

∴ If the simple Interest is $1806, then the time = ¹/₂₅₈ × 1806 years

= ^{1 × 1806}/₂₅₈ years

= ¹⁸⁰⁶/₂₅₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?

(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.

(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.

(5) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(6) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.

(8) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.

(10) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.