Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 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) = 9% per annum

Amount (A) = $10106

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 = $10106 – $6200 = $3906

Thus, Simple Interest = $3906

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 × 3906}/_{6200 × 9}

= ³⁹⁰⁶⁰⁰/₅₅₈₀₀

= 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) = 9% per annum

Simple Interest = $3906 (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 = 9% of Principal

= 9% of $6200

= ⁹/₁₀₀ × 6200

= ^{9 × 6200}/₁₀₀

= ⁵⁵⁸⁰⁰/₁₀₀ = 558

Thus, simple Interest for 1 year = $558

Now,

∵ If the simple Interest is $558, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₈ years

∴ If the simple Interest is $3906, then the time = ¹/₅₅₈ × 3906 years

= ^{1 × 3906}/₅₅₈ years

= ³⁹⁰⁶/₅₅₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(3) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?

(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 9% simple interest?

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.