Determine the amount of money that will be accumulated in an account that pays compound​ interest, given the initial principal of ​$ 29,400 invested at ​2.77% annual interest for 7 years compounded

Question

​(a) daily ​(n​365);
​(b) continuously.

Answer 1

We can use the compound interest formula to calculate the amount of money accumulated in the account.

(a) Daily compounding:

The formula is given by A = P(1 + r/n)^(nt), where:
A = the amount of money accumulated
P = the initial principal
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

Using the given values:
P = $29,400
r = 2.77% = 0.0277
n = 365
t = 7

Plugging the values into the formula, we get:
A = $29,400 * (1 + 0.0277/365)^(365*7)

Calculating this expression gives us:
A ≈ $33,929.57

Therefore, the amount of money that will be accumulated in the account with daily compounding is approximately $33,929.57.

(b) Continuous compounding:

The formula for continuous compounding is given by A = P * e^(rt), where:
A = the amount of money accumulated
P = the initial principal
r = annual interest rate (as a decimal)
t = number of years
e = Euler's number (approximately 2.71828)

Using the given values:
P = $29,400
r = 2.77% = 0.0277
t = 7

Plugging the values into the formula, we get:
A = $29,400 * e^(0.0277*7)

Calculating this expression gives us:
A ≈ $34,023.12

Therefore, the amount of money that will be accumulated in the account with continuous compounding is approximately $34,023.12.