Q1 Deposit 1000 at the end of each month for next 10 years h

Q1: Deposit $1,000 at the end of each month for next 10 years, how much money will I have at the end of 10 years in the following scenarios?

A: 6% interest per year compounded monthly.

B: 8%: interest per year compounded monthly.

Q2: Deposit $1,000 at the end of year 1 and increment the deposit by $100 for the next 4 years, how much money will I have at the end of 5 years in the following scenario?

C: 9% interest per year compounded continuously.

Q3: What is a real-life application of continuous compounding?

Solution

Q1.

A. Monthly interest rate = 6%/12 = 0.5%

Compound interest factor = ((1 + i)ⁿ - 1) / i = ((1+0.5%)¹²⁰ - 1)/0.5% = 163.88 ,  (for 10 years, numbe rof monthly time periods = 10*12 = 120

Fund value at the end of 10 years = 1000*163.88 = 163,880

B. Monthly interest rate = 8%/12 = 0.67%

Compound interest factor = ((1 + i)ⁿ - 1) / i = ((1+0.67%)¹²⁰ - 1)/0.5% = 182.95 ,  (for 10 years, numbe rof monthly time periods = 10*12 = 120

Fund value at the end of 10 years = 1000*182.95 = 182,950