Acouple thinking about retirement decide to put aside $2,100 each year in a savings plan that earns 7% interest. in 10 years they will receive a gift of $29,000 that also can be invested. a. how much money will they have accumulated 30 years from now? (do not round intermediate calculations. round your answer to 2 decimal places.)

310,588.5

Explanation:

As is not said we can assume the 2,100 each year to be paid at the end of the year, and the 7% to be used as a compunded anually rate. So let´s first think just about the 2,100, as they are regulary payments, they can be seen as an anuity inmediate, the formula is as follows:

where sn is the future value of the regular payments, i is the interest rate and n is the number of payments and p is the amount of regular payment so in this particular case we have:

=198,367.65

So now let´s think on the gift of 29,000 as it is paid on 10 years, there will remain 20 years with an investment rate of 7% compounded anually. so there we have the classic formula of future value

where FV is the future value, PV is the present value, i is the interest rate per period, and n is the number of periods. Again in this particular case we have:

so the total amont will be:

total=198,367.65+112,220.85

total=310,588.5

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