Simple Interest
Math MCQs

Question :    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.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4800

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6528

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 = $6528 – $4800 = $1728

Thus, Simple Interest = $1728

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 × 1728}/_{4800 × 6}

= ¹⁷²⁸⁰⁰/₂₈₈₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 6% per annum

Simple Interest = $1728 (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 = 6% of Principal

= 6% of $4800

= ⁶/₁₀₀ × 4800

= ^{6 × 4800}/₁₀₀

= ²⁸⁸⁰⁰/₁₀₀ = 288

Thus, simple Interest for 1 year = $288

Now,

∵ If the simple Interest is $288, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₈ years

∴ If the simple Interest is $1728, then the time = ¹/₂₈₈ × 1728 years

= ^{1 × 1728}/₂₈₈ years

= ¹⁷²⁸/₂₈₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?

(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?

(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.

(5) Betty had to pay $4760 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?

(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(8) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

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