Question

A young couple has just had their first child and they decide to make deposits into an investment account on each of their daughter’s birthdays, starting with her first birthday. Assume that the account will earn an interest rate of 4% p.a. The parents deposit $4,000 on their daughter’s first birthday and plan to increase the size of their deposits by 6% every year. Assuming that the parents make the last deposit on their daughter's 18th birthday, the amount available at that time will be closest to:

Answer 1

The amount available after 18 years will be computed as

FV of growing annuity = First payment*((1+r)^n-(1+g)^n))/(r-g)

[where r= Rate of 4% and g= growth rate of 6%]

= 4000*((1+4%)^18-(1+6%)^18)/(4%-6%)

= 4000*41.42613188

= $165704.53