Simple Interest
Math MCQs

Question :    David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7872

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 = $7872 – $4800 = $3072

Thus, Simple Interest = $3072

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 × 3072}/_{4800 × 8}

= ³⁰⁷²⁰⁰/₃₈₄₀₀

= 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) = $4800

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3072 (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 = 8% of Principal

= 8% of $4800

= ⁸/₁₀₀ × 4800

= ^{8 × 4800}/₁₀₀

= ³⁸⁴⁰⁰/₁₀₀ = 384

Thus, simple Interest for 1 year = $384

Now,

∵ If the simple Interest is $384, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₈₄ years

∴ If the simple Interest is $3072, then the time = ¹/₃₈₄ × 3072 years

= ^{1 × 3072}/₃₈₄ years

= ³⁰⁷²/₃₈₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.

(7) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(8) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?