Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4800

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

Amount (A) = $7824

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 = $7824 – $4800 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{4800 × 9}

= ³⁰²⁴⁰⁰/₄₃₂₀₀

= 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) = $4800

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

Simple Interest = $3024 (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 $4800

= ⁹/₁₀₀ × 4800

= ^{9 × 4800}/₁₀₀

= ⁴³²⁰⁰/₁₀₀ = 432

Thus, simple Interest for 1 year = $432

Now,

∵ If the simple Interest is $432, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₂ years

∴ If the simple Interest is $3024, then the time = ¹/₄₃₂ × 3024 years

= ^{1 × 3024}/₄₃₂ years

= ³⁰²⁴/₄₃₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

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

(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(3) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.

(6) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.