Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9702

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 = $9702 – $6300 = $3402

Thus, Simple Interest = $3402

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 × 3402}/_{6300 × 9}

= ³⁴⁰²⁰⁰/₅₆₇₀₀

= 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) = $6300

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3402 (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 $6300

= ⁹/₁₀₀ × 6300

= ^{9 × 6300}/₁₀₀

= ⁵⁶⁷⁰⁰/₁₀₀ = 567

Thus, simple Interest for 1 year = $567

Now,

∵ If the simple Interest is $567, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₇ years

∴ If the simple Interest is $3402, then the time = ¹/₅₆₇ × 3402 years

= ^{1 × 3402}/₅₆₇ years

= ³⁴⁰²/₅₆₇ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.

(2) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 9% simple interest?

(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(5) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?

(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(7) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?

(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?

(9) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.