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 $8170 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) = 9% per annum

Amount (A) = $8170

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 = $8170 – $4300 = $3870

Thus, Simple Interest = $3870

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 × 3870}/_{4300 × 9}

= ³⁸⁷⁰⁰⁰/₃₈₇₀₀

= 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) = 9% per annum

Simple Interest = $3870 (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 $3870, then the time = ¹/₃₈₇ × 3870 years

= ^{1 × 3870}/₃₈₇ years

= ³⁸⁷⁰/₃₈₇ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(5) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?

(6) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.