Question

Your inheritance will pay you $100,000 a year for five years beginning now. you can invest it in a cd that will pay 7.75 percent annually. what is the present value of your inheritance?

Answer 1

The present value of an inheritance paying $100,000 annually for 5 years with a 7.75% interest rate is calculated by discounting each payment to its current value and summing them up. An example of using compound interest over time is the value of a $1,000 CD after 5 years with a 2% annual interest, which would result in $1,104.08.

Step-by-step explanation:

To determine the present value of the inheritance payments, you need to discount each payment by the interest rate to account for the time value of money. The formula for the present value of an annuity (a series of equal payments at regular intervals) is PV = P * [(1 - (1+r)^-n) / r], where P is the payment amount, r is the interest rate per period, and n is the number of periods.

Given that the payments are $100,000 annually and the interest rate is 7.75% (or 0.0775 when used in the formula), and the number of periods is 5 (since the payments are to be made over five years), the present value is calculated as follows:

1. Discount the first payment of $100,000 by one period: $100,000 / (1 + 0.0775)
2. Repeat this process for each subsequent payment, increasing the number of periods (n) each time.
3. Sum the present values of all the payments.

This would give the present value of the inheritance, which reflects the value in today's dollars of the entire stream of payments you are to receive.

For an example of how compound interest works over time, let's reference the assignment:

If you open a 5-year CD for $1,000 that pays 2% interest, compounded annually, the future value at the end of five years is determined using the formula for compound interest, which is A = P(1+r)^n, where P is the principal amount ($1,000), r is the annual interest rate (2% or 0.02), and n is the number of years (5). The calculation would be as follows:

$1,000(1+0.02)^5 = $1,000(1.10408) = $1,104.08

Just as the future value is calculated for the CD, the present value of the inheritance reflects the current worth of a future sum of money or stream of cash flows given a specified rate of return (7.75% in this case).

Answer 2

Hi there
The formula of the present value of annuity due is
Pv=pmt [(1-(1+r)^(-n))÷r]×(1+r)
Pv present value?
PMT payment per year 100000
R interest rate 0.0775
N time 5 years
So
Pv=100,000×(((1−(1+0.0775)^(
−5))÷(0.0775))×(1+0.0775))
=433,064.19 ....Answer

Hope it helps