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 $6552 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4200

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

Amount (A) = $6552

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 = $6552 – $4200 = $2352

Thus, Simple Interest = $2352

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 × 2352}/_{4200 × 8}

= ²³⁵²⁰⁰/₃₃₆₀₀

= 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) = $4200

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

Simple Interest = $2352 (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 $2352, then the time = ¹/₃₃₆ × 2352 years

= ^{1 × 2352}/₃₃₆ years

= ²³⁵²/₃₃₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.

(2) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?

(5) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(9) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.