提出需求

贷款 100 万，贷款利率为 6%（年利率），贷款期限 15 年。分别计算等额本金和等额本息两种还款方式下每月偿还本金、偿还利息、偿还本息、剩余本金。并对两种还款方式进行比较分析。

加载相关R包

library(ggplot2)
library(dplyr)
library(gt)

参数设置

# 设置贷款金额 value
value = 1000000

# 设置贷款利率 rate
rate = 0.06

# 设置贷款期限 term
term = 15

# 设置还款方式 mode
mode1 = "等额本金"
mode2 = "等额本息"

编写函数

repayment = function(value, rate, term, mode) {
  
  # 年利率换算为月利率
  rate_m = rate / 12
  # 还款期限换算成月
  t = term * 12
  # 生成还款期次向量
  N = 1:t  # 还款期次
  
  # 等额本金模式
  if (mode == "等额本金") {
    MBA = value / t  # 每月应还本金
    MYA = value - MBA * (N-1)  # 截至当月还款前贷款余额
    MYAA = value - MBA * N  # 还贷后剩余本金
    MIA = MYA * rate_m  # 当月应还利息
    MPA = MIA + MBA  # 当月应还本息和
    tbl = data.frame(N, MYA, MBA, MIA, MPA, MYAA, mode)
    colnames(tbl) = c(
      "还款期次", "贷款余额", "应还本金", 
      "应还利息", "应还本息", "剩余本金",
      "还款方式"
    )
  }
    
  # 等额本息模式
  if (mode == "等额本息") {
    # 每月应还的等额本息
    MPB = value * rate_m * (1 + rate_m)^t / ((1 + rate_m)^t - 1) 
    # 截至当月还款前贷款余额
    MYB = value *(1 + rate_m)^(N-1) - MPB * ((1 + rate_m)^(N-1) - 1) / rate_m
    MIB = MYB * rate_m  # 当月应还利息
    MBB = MPB - MIB  # 当月应还本金
    MYBB = MYB - MBB  # 剩余本金
    tbl = data.frame(N, MYB, MBB, MIB, MPB, MYBB, mode)
    colnames(tbl) = c(
      "还款期次", "贷款余额", "应还本金", 
      "应还利息", "应还本息", "剩余本金",
      "还款方式"
    )
  }
  
  # 返回生成的数据框
  return(tbl)

}

生成还款表验证函数

生成等额本金还款表

# 计算等额本金月供
df1 = repayment(
  value = value,
  rate = rate,
  term = term, 
  mode = mode1
)

# 生成还款表
df1[1:6] %>% 
  gt() %>% 
  tab_style(
    style = cell_text(size = px(12)),
    locations = list(
      cells_body(),
      cells_column_labels()
    )
  ) %>% 
  tab_style(
    style = cell_text(align = "center"),
    locations = cells_body(columns = 1)
  ) %>% 
  tab_style(
    style = cell_text(align = "right"),
    locations = cells_body(columns = -1)
  ) %>% 
  fmt_number(
    columns = -还款期次, 
    decimals = 2
  ) %>% 
  tab_style(
    style = cell_fill(color = "#f8f8f8"),
    locations = cells_body(
      rows = (还款期次 %% 2 == 0)
    )
  )

生成等额本息还款表

# 计算等额本息月供
df2 = repayment(
  value = value, 
  rate = rate, 
  term = term, 
  mode = mode2
)

# 生成还款表
df2[1:6] %>% 
  gt() %>% 
  tab_style(
    style = cell_text(size = px(12)),
    locations = list(
      cells_body(),
      cells_column_labels()
    )
  ) %>% 
  tab_style(
    style = cell_text(align = "center"),
    locations = cells_body(columns = 1)
  ) %>% 
  tab_style(
    style = cell_text(align = "right"),
    locations = cells_body(columns = -1)
  ) %>% 
  fmt_number(
    columns = -还款期次, 
    decimals = 2
  ) %>% 
  tab_style(
    style = cell_fill(color = "#f8f8f8"),
    locations = cells_body(
      rows = (还款期次 %% 2 == 0)
    )
  )

两种还款方式比较分析

月还款利息对比

df = rbind(df1, df2)
df %>% 
  ggplot(aes(`还款期次`, `应还利息`, color = `还款方式`)) + 
  geom_line(linewidth = 0.8) + 
  theme(
    legend.title = element_blank(),
    legend.position = "inside",
    legend.position.inside = c(0.89, 0.87)
  )

从上图我们可以可以清洗地发现：等额本金累计还利息比等额本息方式少。 统计结果显示: 等额本金累计还利息452500.00元， 等额本息累计还利息518942.29元， 两者相差66442.29元。

月还本息对比

df %>% 
  ggplot(aes(`还款期次`, `应还本息`, color = `还款方式`)) + 
  geom_line(linewidth = 0.8) + 
  theme(
    legend.title = element_blank(),
    legend.position = "inside",
    legend.position.inside = c(0.89, 0.87)
  )

从图上可以看出，等额本金还款模式前期还款压力较大，后期还款压力逐渐递减，等额本息模式每期还款压力不变。

红线与坐标轴围成的面积即为等额本金下还款总额。同理，蓝线与坐标轴围成的面积即为等额本息下还款总额；很明显蓝线围成的面积更大，即等额本息还款总额较多。

还款总额对比

df %>% 
  group_by(`还款方式`) %>% 
  summarise(`还款总额` = round(sum(`应还本息`), 2)) %>% 
  ggplot(aes(`还款方式`, `还款总额`, fill = `还款方式`)) + 
  geom_bar(stat = "identity") + 
  geom_text(aes(label = `还款总额`), vjust = -0.3) + 
  xlab("")  + 
  guides(fill = "none")

从总还款额同样也能清晰地看出等额本金累计还利息比等额本息方式少。