I try to compute the interest rate of an annuity given the total mortgage, the duration, and the monthly payment.
The formula to calculate the monthly annuity:
i
J = T * --------------
1 - (1 + i)^-n
where T is the total mortgage, i the monthly interest, and J the annuity
Example:
library(purrr)
library(dplyr)
mortgage <- 300000
#annualRate <- ??
duration <- 360
#annuity
ann <- 1108.86
#Use brute force to find the interest rate
annuity <- function(annualRate, mortgage, duration) {
monthRate <- annualRate / 12
ann <- (monthRate / (1- ((1+monthRate)^(-duration)) )) * mortgage
data.frame(rate = annualRate*100, ann = ann)
}
#Try some rates
checkRates <- seq(1,3,0.5)/100
res <- map(checkRates , annuity, mortgage, duration) %>% bind_rows()
res
# rate ann
#1 1.0 964.9186
#2 1.5 1035.3606
#3 2.0 1108.8584
#4 2.5 1185.3627
#5 3.0 1264.8121
Using this brute force technique the interest is 2.0%
Check solution:
annualRate <- 2/100
monthRate <- annualRate / 12
(monthRate / (1- ((1+monthRate)^(-duration)) )) * mortgage
#[1] 1108.858
However, I was wondering if it is possible to calculate the exact interest rate in R without using brute force.
# 1108.86 i
# ------- = --------------
# 300000 1 - (1 + i)^-360
Is it possible to solve this equation using R? Any suggestion is appreciated.
I think you are looking for uniroot. Here is an example usage for your problem:
mortgage <- 300000
duration <- 360
ann <- 1108.86
uniroot(function(x) mortgage * x/12 / (1 - (1+x/12)^(-duration)) - ann,
c(1e-6,1))$root * 100
#[1] 2.000091