Answer
$\$30,000$ more will be from the lump-sum investment than from the annuity.
Work Step by Step
First condition Lump-Sum deposit.
$P=\$30,000$
Rate of interest compounded annually $r=5\%=0.05$.
Time $t=20$ years.
The compounded interest formula is $A=P(1+r)^t$.
Substitute all values into the formula.
$A=30,000(1+0.05)^{20}$
$A=79598.9311543$
Round to the nearest dollar.
$A=\$79599$
Second condition Periodic deposits.
First year $=\$1500$
Second year $=\$1500(1.05)$
Third year $=\$1500(1.05)^2$ and so on.
This is the geometric sequence.
The sum of the all $20$ years deposits is
$S_{20}=\frac{1,500(1-(1.05)^{20})}{1-1.05}$
Simplify.
$S_{20}=\$49598.9311543$
Round to the nearest dollar.
$A=\$49599$.
The difference of both condition is
$\$79599-\$49599=\$30,000$.
