A small business owner contributes $1,000 at the end of each quarter to a retirement account that earns 10% compounded quarterly.

(a) After how many quarterly payments, n, will this annuity account be worth at least $50,000? (Round your answer UP to the nearest quarter.) 17 quarters
(b) Now assume the owner has $50,000 in the same account continuing to earn interest. In addition, the business owner starts making contributions of $3,000 at the end of each quarter into another account with this same interest rate. What will the total value of both accounts be after 15 more years?

Account balance after 15 years is $627,964

Explanation:

Detailed step-wise solution is given in the images attached.

a ) 32.84

b) future value after 15 ears and additional contribution of 3,000 dolalr each

627.964,26‬

Explanation:

Given the formula for an annuity we have to solve for time (n)

C  $1,000.00

timen

rate0.025

PV$50,000.0000

We now solve using logarithmic properties:

n =  32.84  

b)

Value of the 50,000 dollars

Principal50,000.00

time60.00 (15 years x 4 quarter per year)

rate0.02500

Amount219,989.49

Value of the additional contributions:

C3,000.00

time60

rate0.025

FV$407,974.7699

Total:

219,989.49   +  407,974.7699  = 627.964,26‬

simpleton is the answer, this is simpleton work

b is the correct answer