If 26500 dollars is invested at an interest rate of 6 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $
(b) Semiannual: $
(c) Monthly: $
(d) Daily: $

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booksandlegos39 booksandlegos39 · Answer 1 · 2024-05-10T07:14:37-04:00

Answer:

(a) Annual: $35462.1

(b) Semiannual: $35613.8

(c) Monthly: $35744.5

(d) Daily: $35770.4

Step-by-step explanation:

Let's use the formula A = P(1 + r/n)^(nt) to calculate the value of the investment at the end of 5 years for each compounding method, where:

- A is the amount of money at the end of the investment period

- P is the principal amount (the initial investment)

- r is the annual interest rate (as a decimal)

- n is the number of times the interest is compounded per year

- t is the number of years the money is invested

(a) Annual compounding:

A = 26500 * (1 + 0.06/1)^(1*5) = 35462.9778064

(b) Semiannual compounding:

A = 26500 * (1 + 0.06/2)^(2*5) = 35613.7840526

(c) Monthly compounding:

A = 26500 * (1 + 0.06/12)^(12*5) = 35744.5290426

(d) Daily compounding:

A = 26500 * (1 + 0.06/365)^(365*5) = 35770.3764773

Therefore, the value of the investment at the end of 5 years for each compounding method, to the nearest cent, is:

(a) Annual: $35462.1

(b) Semiannual: $35613.8

(c) Monthly: $35744.5

(d) Daily: $35770.4