You deposit $5000 in an account earning 8% interest compounded monthly. How much will you have in the account in 5 years?

Answer:

A = $ 7,449.23

A = P + I where

P (principal) = $ 5,000.00

I (interest) = $ 2,449.23

Step-by-step explanation:

Compound Interest Equation

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Compound Interest Formulas and Calculations:

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r/n)^nt

Calculate Principal Amount, solve for P

P = A / (1 + r/n)^nt

Calculate rate of interest in decimal, solve for r

r = n[(A/P)(^1/nt) - 1]

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]

Formulas where n = 1 (compounded once per period or unit t)

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r)^t

Calculate Principal Amount, solve for P

P = A / (1 + r)^t

Calculate rate of interest in decimal, solve for r

r = (A/P)1/t - 1

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pe^rt

Calculate Principal Amount, solve for P

P = A / ert

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r

Final answer:

To calculate the future amount in the account after 5 years with compound interest, you can use the formula A = P(1 + r/n)^(nt). Plugging in the values, the amount in the account would be $6,803.85.

Explanation:

To calculate the future amount in the account, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• A is the future amount
• P is the principal amount ($5000 in this case)
• r is the annual interest rate (8% in this case)
• n is the number of times the interest is compounded per year (12, since it is compounded monthly)
• t is the number of years

Plugging in the values, we get:

A = 5000(1 + 0.08/12)^(12*5)

Calculating this, we find that the amount in the account after 5 years would be $6,803.85.

Learn more about Compound Interest here:

brainly.com/question/34614903

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