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True
It is very clear,
when you are investing at higher rate of rerurn then their crossponding future cash inflows are also high.
and vise versa.
Your question is odd and unclear. It is similar to asking: If I put $100 in a savings account and the interest increases, will the I have more money in my account in a year? in this case, the answer is yes, duh!
BUT, if you meant to ask: I bought a $100 bond with a coupon rate of5% at face value (and this could as well be a stock, debt, or any cash flow generating instrument). if the market interest rate increased to6%, ie. you can now buy a $100 bond with a coupon rate of6% at par, the5% bond now is worth less than you paid for. Of course, there is math behind all these assumptions but the general idea is that Present Value is inversely proportional to interest.
You can't look at future value because it will always be an estimate based on assumptions.