Question

Six years from today you need $10,000. You plan to deposit $1,600 annually, with the first payment to be made a year from today, in an account that pays a 6% effective annual rate. Your last deposit, which will occur at the end of Year 6, will be for less than $1,600 if less is needed to reach $10,000. How large will your last payment be? Do not round intermediate calculations. Round your answer to the nearest cent.

Anser using BA II Plus Texas Instrument please and thank you.

Answer 1

Value required at the end of Year 6 = $10,000

Annual Deposit = $1,600

Time Period = 6 years

Interest Rate = 6%

To calculate value of last deposit, first we need to calculate value of deposits at the end of year 6 with year 6 deposit as $1,600,

Step-1,

Calculating Value at the end of Year 6,

Using TVM Calculator,

FV = [PV = 0, T = 6, I = 0.06, PMT = 1,600]

Value at Year 6 = $11,160.51

This value exceeds $10,000 by (11,160.51 - 10,000) = $1,160.51

So,

Value of Last Deposit = 1,600 - 1,160.51

Value of Last Deposit = $439.49

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