Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10440

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 = $10440 – $5800 = $4640

Thus, Simple Interest = $4640

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 × 4640}/_{5800 × 10}

= ⁴⁶⁴⁰⁰⁰/₅₈₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 10% per annum

Simple Interest = $4640 (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 = 10% of Principal

= 10% of $5800

= ¹⁰/₁₀₀ × 5800

= ^{10 × 5800}/₁₀₀

= ⁵⁸⁰⁰⁰/₁₀₀ = 580

Thus, simple Interest for 1 year = $580

Now,

∵ If the simple Interest is $580, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₈₀ years

∴ If the simple Interest is $4640, then the time = ¹/₅₈₀ × 4640 years

= ^{1 × 4640}/₅₈₀ years

= ⁴⁶⁴⁰/₅₈₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(3) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?

(4) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(6) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(9) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.