Suppose you invest $250,000 in an annuity that returns 5 annual payments, with the first payment one year from now and each subsequent payment growing by 6%. At an interest rate of 7%, how much is the first annual payment you receive

$54,508.98

Explanation:

Formula of present value of growing annuity: PVGA = A*[(1 - (1+g)^n/(1+i)^n)) / (i-g)

$250,000 = A*[(1 - (1+0.06)^5/(1+0.07)^5)] / (0.07 - 0.06)

$250,000*(0.01) = A*(1 - (1.06)^5/(1.07)^5)

$250,000*(0.01) = A*(1 - 0.9541363)

$2500 = A * 0.045864

A = $2,500 / 0.045864

A = 54508.983080412

A = $54,508.98

So, the amount of the first annual payment i will receive $54,508.98.

cognitive overload: having a lot on your mind impairs decision-making and tends to result in the simplest, but not necessarily best, option being selected.

empathy gaps: overlooking how you might feel in a different situation can result in unnecessary purchases, such as overbuying when shopping for food on an empty stomach.

optimism and overconfidence: wearing rose-tinted glasses and having unrealistic expectations about the future can affect money management and leave you unprepared for a change in circumstance.

instant gratification: seeking instant gratification drives impulsive spending and can undermine long-term planning and savings.

harmful habits: automatic or mindless behaviour can amplify a poor financial decision as it becomes a recurring event.

social norms: we are heavily influenced by the actions of others; while this can be in certain circumstances, it also contributes to the pressure to keep up with the joneses through conspicuous consumption.