Example $1$:

There is an expected payment one year from today of $$1000$ and interest rates for the $1-y$ ear period are vielding $3\%,$ what is the present value for the future payment?

$PV=\frac{1000}{(1+\mathrm{.}03{)}^1}$

$=970\mathrm{.}87$

Example $2$:

A bank wants to increase deposits and is looking to incresase their savings interest rate to achieve this goal. The bank wants to raise $$1,000,000$ through this program and is willing to pay $3\mathrm{.}5\%$ to achieve the goal. The bank expects to reduce this introductory offer in $3-$years and thus all depositors will remove their funds from their account. How much will they have to pay out in interest to achieve their goal?

$FV=1,000,000**(1+\mathrm{.}035{)}^3$

$=1,108,718$

Interest $=108,718$

In Example $$2$ how long could the bank in Example $$2$ keep the accounts active before paying $$1,000,000$ in interest?

In Example #$2$ what interest rate could the bank pay if they wanted to pay $$1,000,000$ in interest in $15$ years?