Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10710

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 = $10710 – $6300 = $4410

Thus, Simple Interest = $4410

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 × 4410}/_{6300 × 10}

= ⁴⁴¹⁰⁰⁰/₆₃₀₀₀

= 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) = $6300

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4410 (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 = 10% of Principal

= 10% of $6300

= ¹⁰/₁₀₀ × 6300

= ^{10 × 6300}/₁₀₀

= ⁶³⁰⁰⁰/₁₀₀ = 630

Thus, simple Interest for 1 year = $630

Now,

∵ If the simple Interest is $630, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₃₀ years

∴ If the simple Interest is $4410, then the time = ¹/₆₃₀ × 4410 years

= ^{1 × 4410}/₆₃₀ years

= ⁴⁴¹⁰/₆₃₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(3) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(5) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(7) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.