Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $9672

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 = $9672 – $6200 = $3472

Thus, Simple Interest = $3472

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 × 3472}/_{6200 × 8}

= ³⁴⁷²⁰⁰/₄₉₆₀₀

= 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) = $6200

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

Simple Interest = $3472 (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 $6200

= ⁸/₁₀₀ × 6200

= ^{8 × 6200}/₁₀₀

= ⁴⁹⁶⁰⁰/₁₀₀ = 496

Thus, simple Interest for 1 year = $496

Now,

∵ If the simple Interest is $496, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₆ years

∴ If the simple Interest is $3472, then the time = ¹/₄₉₆ × 3472 years

= ^{1 × 3472}/₄₉₆ years

= ³⁴⁷²/₄₉₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(2) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

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

(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.

(7) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.