You deposit a single amount of $50,000 in a savings account that pays 7.6% annual interest (compounded quarterly). How much will you have at the end of four and a half years?
A(t) = P(1 + r/n)^nt
P = 50,000
r = 0.076
n = 4 (quarterly)
t = 4.5
A(4.5) = 50000(1 + 0.076/4)^(4(4.5))
A(4.5) = 50000(1 + 0.019)^(18)
A(4.5) = 50000(1.019)^(18)
A(4.5) = 50000(1.40325)
A(4.5) = 70,162.50
50,000 + 70,162.50 = 120,162.50
thats must be wrong right?
because i got 50 000 (1+(14/4*100))^(4*4,5) = 70 162.54 after the four and the half year.
Not adding that with 50 000. Because you earned 20 162.54..
To calculate the amount you will have at the end of four and a half years, we need to use the formula for compound interest.
The formula for compound interest is given by:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $50,000
r = 7.6% or 0.076 (in decimal form)
n = 4 (compounded quarterly)
t = 4.5 years
Let's substitute these values into the formula and calculate the amount:
A = $50,000(1 + 0.076/4)^(4*4.5)
Simplifying the calculation:
A = $50,000(1 + 0.019)^18
A = $50,000(1.019)^18
Now we can calculate the final amount:
A = $50,000 * 1.4312571838256614364898244750485
A = $71,562.86
Therefore, you will have approximately $71,562.86 at the end of four and a half years.