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 $10269 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) = 9% per annum

Amount (A) = $10269

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 = $10269 – $6300 = $3969

Thus, Simple Interest = $3969

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 × 3969}/_{6300 × 9}

= ³⁹⁶⁹⁰⁰/₅₆₇₀₀

= 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) = 9% per annum

Simple Interest = $3969 (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 $3969, then the time = ¹/₅₆₇ × 3969 years

= ^{1 × 3969}/₅₆₇ years

= ³⁹⁶⁹/₅₆₇ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

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

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?

(5) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.

(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?

(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?

(10) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?