Suppose you need $50,000 ten years from now. you plan to make seven equal annual deposits with the first deposit to be made three years from today (e.g. t=3) in an account that yields 11% compounded annually. thus, your last deposit will be made at t=9. the money will remain in your account for one more year; it will continue to accrue interest, but you will not make at deposit at t=10. you will, however, withdraw $50,000 at that time. how much should each annual deposit be? (you might want to draw a time line to be sure you understand when the deposits are made.)

Respuesta :

Answer:

The installment will be for  $ 4,148.010

Explanation:

There will be 7 payment starting at the beginning of the third year therefore, an annuity-due. Then It will capitalize one more year.

Thus, the annuity future value will be the 50,000 discounted one year.

[tex]\frac{Nominal}{(1 + rate)^{time} } = PV[/tex]  

Nominal: 50,000.00

time: 1 year

rate: 11% = 11/100 = 0.11

[tex]\frac{50000}{(1 + 0.11)^{1} } = PV[/tex]  

PV= 45,045.0450

Then we need to solve for the PMT of this annuity:

[tex]FV \div \frac{(1+r)^{time} -1}{rate}(1+r) = C\\[/tex]

PV:  $ 45,045

time:   7 years

rate: 11% = 11/100 = 0.11

[tex]45045.045045045 \div \frac{(1+0.11)^{7} -1 }{0.11}(1+0.11) = C\\[/tex]

C  $ 4,148.010

Q&A Education