$ 2631 is deposited into an account for 15 years. Determine the accumulation if interest is 8.01 % compounded
(a) monthly, (b) daily, (c) continuously.
(Round-off your answers to the nearest cent.)
The accumulation based on
(a) monthly compounding is $ ;
(b) daily compounding is $ ;
(c) continuous compounding is $
Thanks
Pt = Po(1+r)^n.
a. r = (8.01%/12) / 100% = 0.006675 =
Monthly % rate expressed as a decimal.
n = 12 comp./yr * 15 yrs. = 180 comp.
periods.
Pt = 2631(1.006675)^180 = $8713.48.
b. Pt = Po(1+r)^n.
r = (8.01%/360) / 100% = 0.0002225 =
daily % rate expresed as a decimal.
n = 360 comp./yr * 15 yrs. = 5400 comp.
periods.
Plug the calculated values of r and n
into the given EQ and solve.
c. Pt = Po*e^rt.
r = 8.01% / 100% = 0.0801 = Annual % rate expressed as a decimal.
rt = 0.0801/yr * 15yrs. = 1.2015.
Pt = 2631*e^1.2015 = $8748.34.
First name: Henry. not Henry00.
To determine the accumulation of $2631 over 15 years with different compounding periods, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Accumulation (or future value)
P = Principal amount ($2631)
r = Annual interest rate (8.01% or 0.0801)
n = Number of compounding periods per year
t = Number of years
(a) Monthly compounding:
Since interest is compounded monthly, the compounding period (n) would be 12 (12 months per year). Plugging the values into the formula:
A = 2631(1 + 0.0801/12)^(12*15)
A ≈ $5639.23
The accumulation based on monthly compounding is approximately $5639.23.
(b) Daily compounding:
To compute daily compounding, we need to determine the number of compounding periods per year. Since there are 365 days in a year, the compounding period (n) would be 365. Using the formula:
A = 2631(1 + 0.0801/365)^(365*15)
A ≈ $5641.41
The accumulation based on daily compounding is approximately $5641.41.
(c) Continuous compounding:
For continuous compounding, we use the formula:
A = P * e^(rt)
Where:
e = Euler's number (approximately 2.71828)
A = 2631 * e^(0.0801*15)
A ≈ $5696.75
The accumulation based on continuous compounding is approximately $5696.75.
So, to summarize:
(a) The accumulation based on monthly compounding is approximately $5639.23.
(b) The accumulation based on daily compounding is approximately $5641.41.
(c) The accumulation based on continuous compounding is approximately $5696.75.