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Bob makes his first $900 deposit into an IRA earning 7.6% compounded annually on his 24th birthday and his last $900 deposit on his $35th birthday ​(12 equal deposits in​ all). With no additional​ deposits, the money in the IRA continues to earn 7.6% interest compounded annually until Bob retires on his 65th birthday. How much is in the IRA when Bob​ retires?

Respuesta :

Answer:

Total amount = $150160.24

Step-by-step explanation:

The amount deposit by the Bob annually (annuity) = $900

Number of years for which annuity made = 12 years

Inerest rate = 7.6% or 0.076

After 35 years the amount grows at the rate of 7.6% till the age of 65, the total number of years = 30 years.

Now we have to find the total amount after 65 years.

Total amount = annuity [((1+r)^n – 1) / r] × (1+r)^n

Total amount = 900[((1+ 0.076)^12 – 1) / 0.076] × (1+ 0.076)^30

Total amount = $150160.24

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