## Precalculus (6th Edition) Blitzer

$98,888$ dollars.
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.