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
08062670091
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.