Find the matrix by values of an annuity of N10,000 invested at 8% compound over 5 years if the annuity is (a) ordinary (b) Due?

All_for_one

2 years ago

Certainly, let's calculate the future values for both the ordinary and due annuities:

(a) For an ordinary annuity:
Pmt = $10,000
r = 8% or 0.08 (as a decimal)
n = 5 years

FV_ordinary = $10,000 x [(1 + 0.08)^5 - 1] / 0.08
FV_ordinary = $10,000 x [(1.08)^5 - 1] / 0.08
FV_ordinary ≈ $48,425.61

The future value of the ordinary annuity is approximately $48,425.61.

(b) For a due annuity:
Pmt = $10,000
r = 8% or 0.08 (as a decimal)
n = 5 years

FV_due = $10,000 x [(1 + 0.08)^5 - 1] / 0.08 x (1 + 0.08)
FV_due ≈ $52,430.24

The future value of the due annuity is approximately $52,430.24.

So, the matrix values for the annuity of $10,000 invested at 8% compounded over 5 years are:
(a) For the ordinary annuity: $48,425.61
(b) For the due annuity: $52,430.24

All_for_one

2 years ago

To find the future value of an annuity, we can use the future value of an annuity formula:

FV = Pmt x [(1 + r)^n - 1] / r

Where:
FV = Future Value
Pmt = Payment per period
r = Interest rate per period
n = Number of periods

In this case, you want to find the future value of a $10,000 annuity invested at 8% compounded annually over 5 years. Let's calculate it for both ordinary and due annuities:

(a) For an ordinary annuity:
Pmt = $10,000
r = 8% or 0.08 (as a decimal)
n = 5 years

FV_ordinary = $10,000 x [(1 + 0.08)^5 - 1] / 0.08

Calculate this to find the future value of the ordinary annuity.

(b) For a due annuity, the payments occur at the beginning of each period, so you'll need to adjust the formula slightly:
Pmt = $10,000
r = 8% or 0.08 (as a decimal)
n = 5 years

FV_due = $10,000 x [(1 + 0.08)^5 - 1] / 0.08 x (1 + 0.08)

Calculate this to find the future value of the due annuity.

Now, you can calculate both values to find the matrices for the ordinary and due annuities.