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

To calculate the amount of money accumulated, we can use the compound interest formula:

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

Where:
A = the amount of money accumulated
P = the initial principal (or amount invested)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years

(a) For daily compounding (n = 365), the formula becomes:

A = 29,400(1 + 0.0277/365)^(365*7)

Calculating this formula gives:
A ≈ $33977.37

Therefore, the amount of money accumulated in the account after 7 years with daily compounding is approximately $33,977.37.

(b) For continuous compounding, the formula becomes:

A = P * e^(rt)

Where e is Euler's number, approximately 2.71828.

A = 29,400 * e^(0.0277*7)

Calculating this formula gives:
A ≈ $33,930.04

Therefore, the amount of money accumulated in the account after 7 years with continuous compounding is approximately $33,930.04.