spot_rates_to_discount_factors = function(sk){
    ##
    ## Converts spot rates s_k into discount factors d_k
    ##
    ks = 1:length(sk)
    dk = (1+sk)^(-ks)
    return(dk)
}


spot_rates_to_short_rates = function(sk){
    ##
    ## Converts spot rates s_k into short rates r_k
    ##
    rk = c()
    for( k in 1:length(sk) ){
        numer = (1+sk[k])^k
        if( length(rk)==0 ){
            denom = 1
        }else{
            denom = prod(1+rk)
        }
        r_next = numer / denom - 1
        rk = c(rk, r_next)
    }
    return(rk)
}


spot_rates_to_next_years_spot_rates = function(sk){
    n_spots = length(sk)
    js = 2:n_spots
    numer = (1+sk[js])^js
    denom = (1+sk[1])^1
    f_1t = ( numer/denom )^(1/(js-1)) - 1
    return(f_1t)
}

## The first row of the forward rate table (the first row are spot rates): s_k = f_{0, k}
##
sk = c(6.00, 6.45, 6.80, 7.10, 7.36, 7.56, 7.77)
sk = sk/100
print('spot rates:')
print(round(sk * 100, 2))


## The first row of the discount factor table: d_k
##
dk = spot_rates_to_discount_factors(sk)
print('discount rates:')
print(round(dk, 3))

## The first row of the short rate table: r_k
##
rk = spot_rates_to_short_rates(sk)
print('short rates:')
print(round(rk * 100, 2))


## Produce the spot rates in each expected year:
##
print("Expected spot rates each year:")
print(round(sk * 100, 2))

for( rowi in 1:6 ){
    sk_next_year = spot_rates_to_next_years_spot_rates(sk)
    print(round(sk_next_year * 100, 2))
    sk = sk_next_year ## go to the next year
    ##print(round(spot_rates_to_discount_factors(sk), 3)) ## these are the entries in the Discount factor table
}