Question

November Avenue, Inc. wants to have $7,500,000 in an account exactly 16 years from today. They will make equal quarterly payments of $50,000 beginning next quarter and ending in 16 years. The account earns 8.00% p.a., compounded quarterly. November Avenue must have $_______ in its account today.

Answer 1

$315,717.03

Step-by-step explanation:

Let us start by first of determining the future value of $50,000 quarterly payments for 16 years using the future value of an ordinary annuity provided below:

FV=quarterly payment*(1+r)^n-1/r

quarterly payment=$50,000

r=quarterly interest rate=8%/4=2%

n=number of quarterly payments in 16 years=16*4=64

FV=$50,000*(1+2%)^64-1/2%

FV=$50,000*(1.02)^64-1/0.02

FV=$50,000*(3.551493243 -1)/0.02

FV=$50,000*2.551493243 /0.02

FV=$6,378,733.11

The future value above fell short of the target $7,500,000, it means a fixed amount would have to be invested at 8% compounded quarterly for 16 years as well

shortfall=$7,500,000-$6,378,733.11=$1,121,266.89

The present value of the shortfall that would be invested today is computed

PV=FV/(1+r)^n

FV=$1,121,266.89

r=quarterly interest rate=2%

n=number of quarters in 16 years=64

PV=$1,121,266.89/(1+2%)^64

PV=$315,717.03