Question

Question Workspace Check My Work You have savings of $100. You plan to save another $100 at the beginning of each year for 5 years. The account pays annual interest of 8 percent, compounded quarterly. The ending balance (principal plus interest) will be $ at the end of 5 years

Answer 1

Answer:

Total sum due after 5 years = $2,626.9

Explanation:

The sum of 100 that is invested per period(quarterly)for certain number of period is referred is referred  to as an annuity. The total sum that the investment would worth after if interest rate is compounded quarterly for the investment period is referred to as the future value of annuity.

The total sum due can be computed in two stages. The first is to determined how much the annuity investment would worth after 5 years. And the second is to determine how much the single sum of $100 would worth after 5 years.

This done as follows:

The future Value of annuity is computed using the formula below:

FV = A×( (1+r)^n - 1)/r)× (1+r)

A- periodic cash flow invested

r- interest rate per period

n- number of period

FV = future value

r= 8/4= 2%

n= 5×4= 20

FV= 100×(1.02^20 -1)/0.02)×(1.02)= 2478.3

Step 2 : The future value of the value of the Initial lump sum of $100 already existing

FV= A× (1+r)∧n

= 100×(1.02)^20 =148.59

The sum due after the end of the investment period =

2478.3 + 148.59=$2,626.9

Total sum due after 5 years = $2,626.9