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jeka57 [31]
3 years ago
8

Finding Account Balances In Exercise,complete the table to determine the table A for P dollars invested at rate r for t years,co

mpounded n times per year .see Example 3.
n 1 2 4 12 365 continuous compounding
A
p = $1000,r = 4%,t = 20 years
Mathematics
1 answer:
inysia [295]3 years ago
6 0

Answer:

n = 1, A = $2,191.12

n = 2, A = $2,208.04

n = 4, A = $2216.71

n = 12, A = $2222.58

n = 365, A = $2225.44

Compound continuously, A = $2,225.54

Step-by-step explanation:

We are given the following in the question:

P = $1000

r = 4% = 0.04

t = 20 years

Formula:

The compound interest is given by

A = P\bigg(1 + \displaystyle\frac{r}{n}\bigg)^{nt}

where P is the principal, r is the interest rate, t is the time, n is the nature of compound interest and A is the final amount.

For n = 1

A = 1000\bigg(1 + \displaystyle\frac{0.04}{1}\bigg)^{20}\\\\A = \$2,191.12

For n = 2

A = 1000\bigg(1 + \displaystyle\frac{0.04}{2}\bigg)^{40}\\\\A = \$2,208.04

For n = 4

A = 1000\bigg(1 + \displaystyle\frac{0.04}{4}\bigg)^{80}\\\\A = \$2216.71

For n = 12

A = 1000\bigg(1 + \displaystyle\frac{0.04}{12}\bigg)^{240}\\\\A = \$2222.58

For n = 365

A = 1000\bigg(1 + \displaystyle\frac{0.04}{365}\bigg)^{7300}\\\\A = \$2225.44

Compounded continuously:

A = Pe^{rt}\\A = 1000e^{0.04\times 20}\\A = $2,225.54

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