171k views
0 votes
If $21500 is invested at an annual interest rate of 7%, find the value of the investment at the end of 10 years for the following compounding methods.

If $21500 is invested at an annual interest rate of 7%, find the value of the investment-example-1
User Giorgiline
by
7.5k points

1 Answer

4 votes

Answer:

see below

Explanation:

The applicable formula is ...

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

where P is the principal invested (21500), r is the annual interest rate (0.07), n is the number of times per year compounding occurs, and t is the number of years (10).

It is convenient to program a calculator or spreadsheet to compute these values. For the values we want, n = 1, 2, 12, 52, or 365.

  • annual: $42,293.75
  • semi-annual: $42,780.46
  • monthly: $43,207.72
  • weekly: $43,275.31
  • daily: $43,292.78
  • continuous: $43,295.68

__

The formula for continuous compounding is ...

A = Pe^(rt)

_____

As an example of the work, we can use weekly compounding:

A = 21500(1 +.07/52)^(52·10) = 21500(1.00134615385^520)

= 21500(2.01280499) = 43,275.3074 ≈ 43,275.31

(Full calculator precision needs to be used without any rounding until the final answer.)

If $21500 is invested at an annual interest rate of 7%, find the value of the investment-example-1
User Tomasz Stanczak
by
7.7k points