Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $10498

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 = $10498 – $5800 = $4698

Thus, Simple Interest = $4698

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 × 4698}/_{5800 × 9}

= ⁴⁶⁹⁸⁰⁰/₅₂₂₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $5800

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

Simple Interest = $4698 (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 $5800

= ⁹/₁₀₀ × 5800

= ^{9 × 5800}/₁₀₀

= ⁵²²⁰⁰/₁₀₀ = 522

Thus, simple Interest for 1 year = $522

Now,

∵ If the simple Interest is $522, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₂ years

∴ If the simple Interest is $4698, then the time = ¹/₅₂₂ × 4698 years

= ^{1 × 4698}/₅₂₂ years

= ⁴⁶⁹⁸/₅₂₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(8) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?

(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.