Question

1. You start a savings account today by depositing $1,000 in an account. Each year you add 3% to the amount you deposited in the previous year. You do this for 20 years (21 total payments including the payment today.) The interest rate is 6%. How much will you have in the bank at the end of year 20.

Answer 1

You started in saving account from today by depositng $1000 each year. Each year your deposit will increase by 3% per annum and you will deposit a total of 21 paymnets in 20 years including the one today.

Since you make 21 payments in 20 years, we can seperate them by calaculating Future value of 1st payment today and then future value of last 20 payments.

- Future Value in 20 years of 1st payment today:-

Future Value = Payment*(1+r)^n

Where, Payment = $1,000

r = Periodic Interest rate = 6%

n= no of periods = 20

Future Value = $1,000*(1+0.06)^20

Future Value = $1000*3.20713547221

Future Value in 20 years of 1st payment made today= $3207.14

Now, the second paymnet will increase by 3%

Second payment = $1000*(1+3%) = $1030

Calculating the Future value at the end of year 20 of last 20 paymnets using FV of growing annuity formula:-

Where, C= Second payments = $1030

r = Periodic Interest rate = 6%

g = growth rate of payments = 3%

n= no of periods = 20

Future Value = $48,101.83

So, Total Future Value of all 21 payments at the end of 20 years = $3207.14 + $48,101.83

= $51,308.97

So, amount you will have at bank at the end of 20 years is $51,308.97

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