Franco invests some money at 6.9%/a compounded annually and David

invests some money at 6.9%/a compounded monthly. After 30 years, each
investment is worth $25 000. Who made the greater original investment and
by how much?

Franco:

f(1.069)^30 = 25000
f = 3377.60
David:
d(1.00575)^360 = 25000
d = 3173.40

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To determine who made the greater original investment and by how much, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = final amount
P = principle (original investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years

For Franco (compounded annually):
A = $25,000
r = 6.9% = 0.069
n = 1 (compounded annually)
t = 30 years

Now, we can rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

For Franco:
P_Franco = 25,000 / (1 + 0.069/1)^(1*30)

For David (compounded monthly):
n = 12 (compounded monthly)

P_David = 25,000 / (1 + 0.069/12)^(12*30)

By calculating both P_Franco and P_David, we can determine who made the greater original investment. The difference between the two amounts will also tell us by how much one investment is greater than the other.

The difference between Franco and David is 173.25