Tony deposits $2000 into a savings account for his daughter when she is born followed by quarterly payments of $400 at the end of each quarter until there is $30,000 in the fund

Management Apr 25, 2021

Tony deposits $2000 into a savings account for his daughter when she is born followed by quarterly payments of $400 at the end of each quarter until there is $30,000 in the fund. How many years will it take for the savings account to reach $30,000 if it earns 3.5% compounded semi-annually for the entire time?

15.776 years

31.551 years

26.526 years

13.263 years

13.175 years

Expert Solution

Computation of Number of Years using NPER Function in Excel:

=nper(rate,-pmt,pv,fv)/4

Here,

Nper = Number of Years = ?

Rate = ((1+3.5%/2)^2 - 1)/4 = 0.883%

PMT = $400 per quarter

PV = $2,000

FV = $30,000

Substituting the values in formula:

=nper(0.883%,-400,2000,30000)/4

Nper or Number of Years = 15.736 Years

The correct option should be A "15.776 years". The difference is due to rounding off figures.

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