Question

1. Bill and Martha open a savings account for their granddaughter, Ariel on the day she is born.  They make annual deposits of $2,000 into this account each year on her birthday.  Assume the account earns an interest 5% compounded annually.
   1. How much money will be in the account when Ariel turns 18?
   2. Bill and Martha are travelling the year Ariel turns 12 and are unable to make the $2,000 deposit.  How much money will have Ariel have in her account when she turns 18?

Answer 1

Given,

Annual deposits (A) = $2000

Interest rate (r) = 5% or 0.05

No. of annual deposits (n) = 18

Solution :-

(a)

Future value = A/r x [(1 + r)ⁿ - 1]

= $2000/0.05 x [(1 + 0.05)¹⁸ - 1]

= $40000 x [(1.05)¹⁸ - 1]

= $40000 x [2.40661923359 - 1]

= $40000 x 1.40661923359 = $56264.769

(b)

At the age of 12, no. of years remaining would be 6 years.

Future value of $2000 deposit = $2000 x (1 + 0.05)⁶

= $2000 x (1.05)⁶

= $2000 x 1.34009564 = $2680.19128

Money in the account at age 18 = Future value in part (a) - Future value of $2000 deposit

= $56264.769 - $2680.19128 = $53584.58