Question

A couple 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.)

Answer 1

Answer:

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:

$s_{n}=p*\frac{(1+i)^{n}-1 }{i}$

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:

$s_{n}=2,100*\frac{(1+0.07)^{30}-1 }{0.07}$

$s_{n}=$=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

$FV=VP*(1+i)^{n}$

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:

$FV=29,000*(1+0.07)^{20}$

$FV=112,220.85$

so the total amont will be:

total=198,367.65+112,220.85

total=310,588.5