Question

Over fourteen years, Casey has saved $7200 by authorizing $30 to be deduced at the end of every month through a payroll deduction plan at his work. The money was sent to his savings account to be invested.

a) what is the nominal annual rate of interest compounded monthly on the savings plan?

b) If, after the fourteen years, he withdraws $135 at the end of each month, what is the term of an annuity?

Answer 1

a)

future value of annuity = P*[(1+r)^n - 1 / r ]

where r = rate of interest

n = number of periods = 14*12 = 168

P = monthly deposit

7200 = 30*[(1+r)^168 - 1 / r]

using financial calculator or rate function in excel we can find 'r'

monthly rate = 0.405%

nominal annual rate = 0.405*12 = 4.86%

b)

this can be solved using nper function of excel

term = 60.21months lets say 60months(rounded off) i.e., 5 years