Answer
$98,888$ dollars.
Work Step by Step
Step 1. For the lump-sum investment, we have
$P_1=40,000, r=0.065, n=1, t=25$
Thus
$A_1=P_1(1+r)^{t}=40,000(1+0.065)^{25}\approx193,108$
Step 2. For the annuity, we have
$P_2=1600, r=0.065, n=1, t=25$
Thus
$A_2=\frac{P_2[(1+r)^t-1]}{r}=\frac{1600[(1+0.065)^{25}-1]}{0.065}\approx94,220$
Step 3. Thus, the difference between the two investments is
$A_2-A_1=193,108-94,220=98,888$ dollars.
