Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4200

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

Amount (A) = $6888

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 = $6888 – $4200 = $2688

Thus, Simple Interest = $2688

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 × 2688}/_{4200 × 8}

= ²⁶⁸⁸⁰⁰/₃₃₆₀₀

= 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) = $4200

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

Simple Interest = $2688 (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 $4200

= ⁸/₁₀₀ × 4200

= ^{8 × 4200}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $2688, then the time = ¹/₃₃₆ × 2688 years

= ^{1 × 2688}/₃₃₆ years

= ²⁶⁸⁸/₃₃₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?

(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

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

(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.

(7) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(9) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(10) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.