Question

If $1000 is invested at 4% interest, find the value of the investment at the end of 9 years if the interest is compounded as follows.

a) Annually
b) Semiannually
c) Monthly
d) Weekly

Answer 1

The value of the investment at the end of 9 years with different compounding frequencies is: a) $1485.96 (annually), b) $1488.87 (semiannually), c) $1490.46 (monthly), d) $1490.92 (weekly).

Step-by-step explanation:

To find the value of the investment at the end of 9 years with different compounding frequencies, we can use the formula:

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

where A is the final amount, P is the principal amount, r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

1. a) For annual compounding, the formula becomes: A = 1000(1+0.04/1)^(1*9) = $1485.96
2. b) For semiannual compounding, the formula becomes: A = 1000(1+0.04/2)^(2*9) = $1488.87
3. c) For monthly compounding, the formula becomes: A = 1000(1+0.04/12)^(12*9) = $1490.46
4. d) For weekly compounding, the formula becomes: A = 1000(1+0.04/52)^(52*9) = $1490.92