For the $1,000 cost project:

(a) You would have to borrow $100 at an interest rate of 10% in order to take the project. If you take the project, you will therefore have $1,000 . 1.08 − $110 = $970 next period. If instead you invest $900 at the 4% savings rate, you will receive only $936. You should definitely take the project.

(b) There is a trade-off between investing a smaller sum in the bank and a larger sum in the project now. Say you invest I. If you put it into the bank, you receive I . (1 + 4%) = I . 1.04. If you put I into the project, you receive $1,000 . 1.08 from the project, borrow ($1,000 − I) at an interest rate of 10%. Therefore, you must solve I . 1.04 = $1,000 . 1.08 − ($1,000 − I) . 1.1 The solution is I ≈ $333.33, which means that if you want to consume more than $1,666.67, you should not take the project. Check: [1] If you consume $1,700, you have a remaining $300 to invest. The bank would pay $312 next year. The project would pay off $1,080, but you would have to borrow $700 and pay back $770, for a net of $310. You should not take the project. [2] If you consume $1,600, you have a remaining $400 to invest. The bank would pay $416 next year. The project would pay off $1,080, but you would have to borrow $600 and pay back $660, for a net of $420. You should take the project.