Question

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?

Answer 1

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