Lamar has received $2,000 each year for college
from his
grandmother for the four years that he was in high
school. He has
deposited the money on the same day each year in
an account that
pays 8% interest, compounded annually. How
much money has he saved?
A $7,012.22
B $9,012.22
C $720.98
D $9,733.20
I do not understand but I think it MIGHT be A?
Gee -- doesn't 2,000 times 4 = $8,000?
Then he has interest on top of that.
SO than D or B? :)
To find out how much money Lamar has saved over the four years, we need to calculate the future value of his deposits. We can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where:
FV is the future value
P is the initial deposit
r is the interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, Lamar received $2,000 each year for four years, so the initial deposit (P) is $2,000. The interest rate (r) is 8% or 0.08, and the interest is compounded annually (n=1). The time period (t) is also four years.
Let's plug in the values into the formula:
FV = 2000(1 + 0.08/1)^(1*4)
= 2000(1 + 0.08)^4
= 2000(1.08)^4
≈ 2000(1.3605)
≈ 2721
So, Lamar has saved approximately $2,721.
Since none of the given options match this amount exactly, it seems there may be an error in the answer choices.
To solve this problem, we need to calculate the future value of the annual deposits over four years with an 8% interest rate. The formula for calculating the future value of a compound interest is:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value (initial deposit)
r = Interest rate (in decimal form)
n = Number of years
In this case, here's how we can find the future value:
1. Convert the interest rate to a decimal: 8% = 0.08.
2. Calculate the future value for each year's deposit separately:
Year 1: PV = $2,000, r = 0.08, n = 1
FV1 = $2,000 * (1 + 0.08)^1
Year 2: PV = $2,000, r = 0.08, n = 1
FV2 = $2,000 * (1 + 0.08)^2
Year 3: PV = $2,000, r = 0.08, n = 1
FV3 = $2,000 * (1 + 0.08)^3
Year 4: PV = $2,000, r = 0.08, n = 1
FV4 = $2,000 * (1 + 0.08)^4
3. Add up the future values of each year to find the total savings:
Total Savings = FV1 + FV2 + FV3 + FV4
Now let's calculate the answer:
Year 1: FV1 = $2,000 * (1 + 0.08)^1 = $2,160
Year 2: FV2 = $2,000 * (1 + 0.08)^2 = $2,332.80
Year 3: FV3 = $2,000 * (1 + 0.08)^3 = $2,526.82
Year 4: FV4 = $2,000 * (1 + 0.08)^4 = $2,743.04
Total Savings = $2,160 + $2,332.80 + $2,526.82 + $2,743.04 = $9,762.66
So the correct option is not A, but rather D: $9,733.20.