Question

You are planning to make annual deposits of $6,090 into a
retirement account that pays 9 percent interest compounded monthly.
How large will your account balance be in 30 years? **(Do not
round intermediate calculations and round your final answer to 2
decimal places, e.g., 32.16.)**

Answer #1

**Given,**

**Annual deposits (A) = $6090**

**Interest rate = 9% or 0.09**

**Number of years (n) = 30 years**

**Solution :-**

**Effective annual rate (r) = [1 + (interest
rate/12)] ^{12} - 1**

**= [1 + (0.09/12)] ^{12} - 1**

**= [1 + 0.0075] ^{12} - 1**

**= [1.0075] ^{12} - 1**

**= 1.0938068976 - 1 = 0.0938068976**

**Now,**

**Future value = A/r x [(1 + r) ^{n} -
1]**

**= $6090/0.0938068976 x [(1 + 0.0938068976) ^{30}
- 1]**

**= $6090/0.0938068976 x [(1.0938068976) ^{30} -
1]**

**= $6090/0.0938068976 x [14.730576094362 -
1]**

**= $6090/0.0938068976 x 13.730576094362 =
$891397.23**

**Your account balance will be $891397.23 in 30
years.**

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