Solution:
The present value of $100 in 10 years at an interest rate of 0% is $100. It is because there is no return in the form of interest on the investment.
Present Value = Future Value/ (1+interest)years
PV = 100/(1+0)10
= 100/110=100
If the interest rate is other than zero then the value increases every time.
If the interest rate is zero, then $100 to be paid in 10 years has a present value that is
less than $100, more than $100, exactly $100, Indeterminate.
Summary:
If the interest rate is zero, then $100 to be paid in 10 years will be $100.
Certainly! Based on the provided article discussing present value, interest rates, and future value calculations, let's delve into the concepts mentioned:
Present Value (PV):
The present value represents the current worth of a future sum of money, considering a specified rate of return (interest rate). The formula used is: [PV = \frac{FV}{(1 + r)^n}] Where:
- (PV) = Present Value
- (FV) = Future Value
- (r) = Interest Rate
- (n) = Number of periods
Future Value (FV):
The future value is the value of an asset or cash at a specified date in the future, based on an assumed rate of growth or interest rate.
Interest Rate:
The interest rate is the proportion of a loan that is charged as interest to the borrower, typically expressed as an annual percentage of the principal.
Present Value Calculation at 0% Interest Rate:
In the case where the interest rate is 0%, the formula simplifies to: [PV = \frac{FV}{(1 + 0)^n} = \frac{FV}{1}] Therefore, the present value ((PV)) in this scenario is equal to the future value ((FV)), as there's no consideration for growth or interest accumulation.
Impact of Non-Zero Interest Rates:
When the interest rate is greater than zero, the present value of money decreases as the interest rate rises. Conversely, as the interest rate decreases, the present value of money increases.
Scenario with $100 to be Paid in 10 Years at 0% Interest:
In the article's scenario, if $100 is to be paid in 10 years with a 0% interest rate, the present value will remain exactly $100. This is because there's no factor to adjust or discount the future value, as there's no return or interest on the investment.
Conclusion:
- At a 0% interest rate, the present value of $100 to be received in 10 years will indeed be $100, following the formula: (PV = \frac{FV}{(1 + 0)^n}).
Understanding present value, future value, and their relationships with interest rates is fundamental in financial planning, investment decisions, and evaluating the worth of future cash flows. These concepts are essential in various financial calculations and analyses.
