Gabriel has an annuity that pays $1,310 at the beginning of each year. If the economy grows at a rate of 1.95% quarterly, what is the value of the annuity if he received it in a lump sum now rather than over a period of eight years?

For this case we have the following expression:

P (t) = P * (1 + r / n) ^ (n * t)

Where,

P: initial amount

r: interest

n: periods

t: time in years

Substituting values we have:

P (8) = 1310 * (1 + 0.0195 / 4) ^ (4 * 8)

P (8) = $ 1530.58

Answer:

the value of the annuity is:

P (8) = $ 1530.58