Question

Information: $250 deposit upfront $500 yearly fee for 5 years

1. Assuming an interest rate of 5% per year over a period of 5 years on the money put in the bank, how much will A-Design have in its bank account at the end of the first year?

2. Assuming an interest rate of 5% per year over a period of 5 years on the money put in the bank, calculate the simple interest and the compound interest earned by A-Design at the end of the fifth year?

3. Assuming an interest rate of 5% per year compounded every 6 months over a period of 5 years on the money put in the bank, how much will A-Design have in its bank account at the end of the fifth year?

4. Assuming an interest rate of 5% per year compounded monthly over a period of 5 years on the money put in the bank, how much will A-Design have in its bank account at the end of the fifth year?

Answer 1

Answer (1) $250 deposit in advance along with $500 yearly.

* Assuming that $500 will be deposit at end of every year as nothing is clear about amount to be deposit either begining of year or end of year. Hence assumed that $500 will be deposited at end of every year for 5 years.

Simple interest formula = P×R×T / 100

Simple interest on end of first year on $250 × 5% × 1 / 100 is $12.5

Total amount in bank account in end of 1st year is $250 + $12.5 + $500 = $762.5

Answer (2) Simple interest

1st year interest = 250 × 5% × 1 /100 = $12.5

2nd year interest = (250 + 500) × 5% × 1 / 100 = $37.5

3nd year interest = ( 250 + 500 + 500 ) × 5% × 1 / 100 = $ 62.5

4th year interest = (250+500+500+500) × 5% × 1 / 100 = $87.5

5th year interest = (250+500+500+500+500)= 2250× 5% × 1 / 100 = $112.5

Principle amount is $2250.

Simple interest for 5 years is 12.5 + 37.5 + 62.5 + 87.5 + 112.5 = $312.5

Total amount = $2250 + $312.5 = $2562.5

Compound Interest ( Assumed to compounded yearly )

Compound interest formula

A = P ( 1 + r ) ^t

Advance deposit $250 along with $500 deposit yearly ( end of year )

1st year compounded interest

A = 250 ( 1+0.05 )¹ = $262.5

2nd year compounded interest

Principle amount = 262.5 + 500 = $762.5

A = 762.5 ( 1+0.05 )¹ = $800.625

3rd year compounded interest

Principle amount = 800.625 + 500 = $1300.625

A = 1300.625 ( 1+0.05 )¹ = $1365.656

4th year compounded interest

Principle amount = 1365.656 + 500 = $ 1865.656

A = 1865.656 × (1+0.05)¹ = $1958.939

5th year compounded interest

Principle amount = 1958.939 + 500 = $2458.939

Total Amount = 2458.939 × (1+0.05)¹= $2581.89

Total amount at end of 5th year is $2582 ( rounded off )

Simple interest at end of 5th year = $2562.5

Compound Interest at end of 5th year = $2582

Answer (3) Compound Interest ( Compounded every 6 months )

A = P ( 1 + r/2 )^2×t

1st year compounded interest

A = 250 ( 1+0.025 )^1×2 = $262.66

2nd year compounded interest

Principle amount = 262.66 + 500 = $762.66

A = 762.66 ( 1+0.025)² = $802.27

3rd year compounded interest

Principle amount = 801.27 + 500 = $1301.27

A = 1301.27 ( 1+0.025 )² = $1367.15

4th year compounded interest

Principle amount = 1367.15 + 500 = $ 1867.15

A = 1867.15 × (1+0.025)² = $1961.67

5th year compounded interest

Principle amount = 1961.67 + 500 = $2461.67

Total Amount = 2461.67 × (1+0.025)² = $2586.29

Compound interest at End of 5th year when compounded every 6 months then Total amount in bank account at end of 5th year is $2586 (Rounded off ).

Answer 3 : When interest is compounded monthly.

A = P ( 1+r/12)¹² = P ( 1+0.05/12)¹² =

A= P (1+0.004167)¹²

Repeat above 2nd answer with this formula.

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