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Bob makes his first $ 1 comma 700 deposit into an IRA earning 7.5 % compounded annually on his 24th birthday and his last $ 1 comma 700 deposit on his 44th birthday ​(21 equal deposits in​ all). With no additional​ deposits, the money in the IRA continues to earn 7.5 % interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob​ retires?

Respuesta :

Answer:

amount = $707744.50

Explanation:

given data

PMT = $1700

rate = 7.5% = 0.075

number of period = 21

we find here future value that is express as

future value =  PMT × [tex]\frac{(1+r)^t -1}{r}[/tex]    ........1

here r is rate and t is time period that is 21

put here value

future value =  1700 × [tex]\frac{(1+0.075)^{21} -1}{0.075}[/tex]

future value = $80839.30

and

the future value is then compound annually till his 65th birthday

so time period t = 30

so

amount in IRA

amount = future value  × [tex](1+r)^{t}[/tex]

here r is rate and t is time

put here value

amount = 80839.30 × [tex](1+0.075)^{30}[/tex]

amount = $707744.50

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