solve without excel It is known that an investment of $400 will increase to $320
ID: 2820369 • Letter: S
Question
solve without excel It is known that an investment of $400 will increase to $3200 at the end of 20 years. Find the sum of present values of three payments of $20,000 each which will occur at the end of 20, 40, and 60 years. Q2. (a) (6 marks) (b) Simon wishes to accumulate $50,000 in an investment fund at the end of 20 years. If he deposits $1000 in the fund at the end of each of the first 10 years and $1000+X in the fund at the end of each of the second 10 years, find X if (6 marks) the fund earns 7% effective interest rate.Explanation / Answer
PV = FV/(1+r)^n
PV - Present value
FV - Future value
r - Interest rate
n - no. of periods
400 = 3200/(1+r)^20
r = 10.9569%
Sum of present values = 20000/(1+10.9569%)^20 + 20000/(1+10.9569%)^40 + 20000/(1+10.9569%)^60
= $2851.59
b.
Value of first $1000,
FV of annuity = P*[((1+r)^n - 1)/r]
P - Periodic payment
r - rate per period
n - number of periods
FV of annuity at the end of 10 years = 1000*(((1+0.07)^10 - 1)/0.07)
= $13816.44796
Value at the end of 20 years = 13816.45*(1+0.07)^10 = $27179.04436
Value required = 50000 - 27179.04436 = $22820.95564
This amount should be accumulated in the second 10 years,
Using future value of annuity formula
22820.95564 = (1000+x)*(((1+0.07)^10 - 1)/0.07)
22820.95564 = (1000+x)*13.81644796
x = $651.72
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