Respuesta :
Answer:
$2,969.22
Explanation:
Equal principal repayment=$2,500/5
Equal principal repayment=$500
The fact that Jeremy's son repaid $517.50 at the end of the 5th year, means that the interest paid in year 5 is the difference between the amount repaid($517.50) and the equal principal repayment($500)
interest paid in year 5=$517.50-$500=$17.50
That also means that the balance outstanding at the beginning of year 5( at the end of year 4) is $500, which effectively means that the interest rate on the loan is the determined thus:
interest paid in year 5=balance at the end of year 4*interest rate
$17.50=$500*interest rate
interest rate=$17.50/$500
interest rate=3.50%
The schedule of repayment is attached
The first repayment would be invested for 4 years, since it is occurring at the end of year 1( in years 2-5), the year 2 repayment would be invested for only 3 years and so on.
FV value of reinvestment of repayment=$587.50*(1+3.50%)^4+$570.00*(1+3.5%)^3+$552.50*(1+3.5%)^2+$535.00*(1+3.5%)^1+$517.50
FV value of reinvestment of repayment=$2,969.22
Answer:
The amount the fund accumulated to by the end of the 5 years is $2,648.23.
Explanation:
Step 1: Calculation of interest rate
The interest rate can be calculated using the following RATE function in Excel:
Interest rate = RATE(nper,pmt,-pv,fv,type) .............(1)
Where;
nper = number of periods = number of years = 5
pmt = Fixed annual payments = Amount repaid by his son at the end of the 5th year = $517.50 = 517.50
pv = present value = Loan amount = $2,500 = 2500
fv = future value = desired cash balance after last payment = 0
type = when payments are due (0 = end of period. 1 = beginning of period) = 0
Substituting the values into equation (1), we have:
Interest rate RATE(5,517.50,-2500,0,0) .................. (2)
Inputting =RATE(5,517.50,-2500,0,0) into a cell in an excel sheet (Note: as done in the attached excel file), we have:
Interest rate = 1.16%
Step 2: Calculation of the amount the fund accumulated to by the end of the 5 years
This can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (3)
Where,
FV = Future value = The amount the fund accumulated to by the end of the 5 years =
M = Fixed annual payments = $517.50
r = Interest rate = 1.16%, or 0.0116
n = number of years = 5
Substituting the values into equation (3), we have:
FV = $517.50 * (((1 + 0.0116)^5 - 1) / 0.0116)
FV = $517.50 * 5.11735342258641
FV = $2,648.23
Therefore, the amount the fund accumulated to by the end of the 5 years is $2,648.23.
