Question

Lisa Simpson, age 8 genius, deposits $100 today and plans to continue making additional deposits of $100 at the end of each quarter for the next 13 years into a special off shore account that pays a tax-free 6% nominal annual rate coumpounded quarterly.  At the end of 13 years after making 53 deposits, Lisa pays to use the money to go to Europe "to find herself".  How much will Lisa have for her future trip to Europe? Round your answer to the nearest dollar.

Answer 1

Answer: $8,009.3

Explanation:

Given that,

Deposits(P) = $100 today (Annuity amount)

Additional deposits = $100 end of each quarter for the next 13 years

nominal annual rate = 6% compounded annually

$Quarterly\ rate(r) = \frac{0.06}{4}$

                               = 0.015

No. of deposits (n) = 53

Payments are made at end of quarter. So future Value of annuity formula will become applicable.

Future value of annuity due = $P\times\frac{(1+r)^{n}-1}{r}$

                                                            = $100\times\frac{(1+0.015)^{53}-1}{0.015}$

                                                            = 100 × 80.09

                                                            = $8,009.3

Therefore, she will have $8009.38 for her trip.