Question

My Notes AR Your Teacher A small business owner contributes $3000 at the end of each quarter to a retirement account that earns compounded quarterly (a) How long will it be until the account is worth $150,000? (Round your answer UP to the nearest quarter.) X quarters (b) Suppose when the account reaches $150,000, the business owner increases the contributions to $7000 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)

Answer 1

Answer

(a) Number of periods is 35 quarter.

(b) Total value after 15 years is $1,274,186.

Explanation

Annuity = $3000

Future value (FV) = $150,00

Quarter rate = 8% / 4 = 2%

(a) Number of periods (n) is computed using the equation given below:

FVIFA (r, n) = Future value / Annuity

FVIFA (2%, n) = $150,000 / $3000

= 50

After verifying the FVIFA table, the value 50 at the rate 2% is around 35 period.

hence, the number of periods is 35 quarter.

(b) Number of quarters = 15 * 4 = 60 quarter

Future value (FV) is computed using the equation given below:

FV = {$150,000 * (1 + r) ⁿ} + {Annuity * FVIFA (r, n)}

= {$150,000 * (1 + 8%) ¹⁵} + {$7,000 * FVIFA (2%, 60)}

= {$150,000 * 3.17217} + {$7,000 * 114.0515}

= $475,825.50 + $798,360.50

= $1,274,186

Hence, the FV is $1,274,186.