Question

A small business owner contributes $1000 at the end of each quarter to a retirement account that earns 8% compounded quarterly.

(a) How long will it be until the account is worth $150,000? (Round your answer UP to the nearest quarter.)
I'm coming up with 70.0055 but the answer is incorrect.  

(b) Suppose when the account reaches $150,000, the business owner increases the contributions to $5000 at the end of each quarter. What will the total value of the account be after 15 more years? (Round your answer to the nearest dollar.)
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Answer 1

Answer a.

Desired Sum = $150,000
Quarterly Payment = $1,000
Annual Interest Rate = 8%
Quarterly Interest Rate = 2%

Let n be the number of quarters required to achieve the desired sum

$1,000 * FVIFA(2%, n) = $150,000

Using financial calculator:
I = 2%
PV = 0
PMT= -1000
FV = 150000

N = 70.005

Number of Quarters = 70.005
Number of Years = 70.005/4
Number of Years = 17.50

So, it will take 17.50 years to accumulate $150,000

Answer b.

Current Balance = $150,000
Quarterly Payment = $5,000
Period = 15 years or 60 quarters
Quarterly Interest Rate = 2%

Accumulated Sum after 15 years = $150,000 * FVIF (2%, 60) + $5,000 * FVIFA(2%, 60)

Using financial calculator:
N = 60
I = 2%
PV = -150000
PMT = -5000

FV = 1062412

So, account balance after 15 years will be $1,062,412