Question

If 1200 dollars is invested in an account for 10 years. Find the value of the investment at the end of 10 years if the interest is:

(a) 5.2% compounded annually: $
(b) 5.2% compounded semiannually: $
(c) 5.2% compounded quarterly: $
(d) 5.2% compounded monthly: $
(e) 5.2% compounded daily (ignore leap years): $

Answer 1

To find the future value of $1200 invested over 10 years with a 5.2% interest compounded quarterly, the formula A = P(1 + r/n)^(nt) gives approximately $1972.34. If compounded daily, the final amount is approximately $1978.47.

Step-by-step explanation:

When calculating the future value of an investment with compound interest, we use the formula A = P(1 + r/n)^(nt), where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal form).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for in years.

For the case of $1200 invested at an interest rate of 5.2% compounded quarterly:

A = 1200(1 + 0.052/4)^(4*10)
A = 1200(1.013)^40
A = 1200(1.643619463)
A = $1972.34 (approximately)

And for the investment compounded daily (ignoring leap years), using 365 days in a year:

A = 1200(1 + 0.052/365)^(365*10)
A = 1200(1.000142465)^3650
A = 1200(1.64872127)
A = $1978.47 (approximately)