Question

Problem 1.3 In this example we will compare how the return to saving depends on how frequently interest is compounded. We say that interest is compounded annually if it is only paid once, at the end of the year. If the interest rate is the total return on such an investment is 1+ , reflecting interest and principal. If interest is compounded semi-annualy (twice a year), the return after the first six months is equal to 1+r/2. Assuming that both principal and interest are re-invested, the total return at the end of the year is then (1+r/2). More generally, if interest is compounded n times during the year the return is R(n) = (1+r/n)" Write down & Julia function that calculates R(n,r) as a function of n and r. Then create a vector that records the return on saving for all integer values of n between 1 and 100 and r = 0.10. Do this in two ways: once using a for-loop and once using vectorization. Problem 1.4 Suppose that interest rates are equal to -0.02 in odd years (1, 3, 5, ...) and 0.05 in even years (2, 4, 6 ...). Suppose you deposit $100 in year 1, and so you have a balance of 100%(1-0.02) after the first year, 100%(1 -0.02)x(1+0.05) after the second year, 100 x (1 -0.02) (1+0.05) x (1 -0.02) at the end of the third year, etc. Use a for-loop and an if/else conditional statement to calculate the balance on the account at the end of each of the 50 years following the deposit. (Hint: use isodd(x) to determine if the variable x is odd and the recursion B(t) = B(t-1)×(1+r(t)) to calculate the balance at t as a function of last period's balance and the period t interest rate.) Plot the balance on the account against time.

in julia

Answer 1

ANSWER;

function R(r, n)
return (1+r/n)^n
end

r = 0.10

# using loop
loopAns = Float64[] # empty vector
for i = 1:100 # for-loop
push!(loopAns, R(r,i)) # push return value
end
println("Calcuated return using for-loop\n",loopAns)

# using vectorization
n = collect(1:100) # vector containing values from 1 to 100
vectorAns = R.(r,n)
println("Calcuated return using vectorization\n",vectorAns)

Output:

1.li Result $julia main.jl Calcuated return using for-loop (1.1, 1.1025, 1.10337, 1.10381, 1.10408, 1.10426, 1.10439, 1.10449, 1.10456, 1.10462, 1.10467, 1.10471, 1.10475, 1.10478, Calcuated return using vectorization [1.1, 1.1025, 1.10337, 1.10381, 1.10408, 1.10426, 1.10439, 1.10449, 1.10456, 1.10462, 1.10467, 1.10471, 1.10475, 1.10478,