an inheritance will be 20000. the interest rate for the the time value of money is 7%. How much is the inheritance worth now, if it will be received
a) in 5 years?
b)in 10 years?
c)in 20 years
I know i'm supposed to use F=P(1+i)^n
or P=F(1+i)^-n but I am not sure if the problem is asking me for the future value in 5 yrs or the present value of how much the money is worth now if the inheritance is given in 5,10,20 years.
And are all parts of the question independent. Or when I do partb), do I add the value I got in part a to it.
first one:
PV = 20000(1.07)^-5
= 14259.72
you try the other two.
To calculate the future value of the inheritance, you can use the formula F = P(1 + i)^n, where F is the future value, P is the present value (inheritance amount), i is the interest rate, and n is the number of years.
a) If you want to find the future value in 5 years, you need to use the formula F = P(1 + i)^n, where P is the inheritance amount (20000), i is the interest rate (7% or 0.07), and n is the number of years (5).
F = 20000(1 + 0.07)^5
F = 20000(1.07)^5
F ≈ 28,338.19
So, the future value of the inheritance after 5 years would be approximately $28,338.19.
b) If you want to find the future value in 10 years, you need to use the same formula as before but with n = 10.
F = 20000(1 + 0.07)^10
F ≈ 38,697.38
The future value of the inheritance after 10 years would be approximately $38,697.38.
c) If you want to find the future value in 20 years, you again use the same formula with n = 20.
F = 20000(1 + 0.07)^20
F ≈ 76,122.99
The future value of the inheritance after 20 years would be approximately $76,122.99.
Now, regarding your question about the independence of the parts: each part (a, b, and c) is independent, meaning you can calculate the future value for each duration (5 years, 10 years, and 20 years) separately. There is no need to add the values from part a to part b or part c.
To determine the worth of the inheritance now, you need to calculate the present value using the formula P = F / (1+i)^n, where P is the present value, F is the future value, i is the interest rate, and n is the number of years.
a) In 5 years:
P = 20000 / (1 + 0.07)^5
P ≈ 14438.56
So the inheritance is worth approximately $14,438.56 now if it will be received in 5 years.
b) In 10 years:
P = 20000 / (1 + 0.07)^10
P ≈ 11590.05
So the inheritance is worth approximately $11,590.05 now if it will be received in 10 years.
c) In 20 years:
P = 20000 / (1 + 0.07)^20
P ≈ 8435.93
So the inheritance is worth approximately $8,435.93 now if it will be received in 20 years.
Each part of the question is independent. You don't need to add the value obtained in part a to part b or c. Each calculation is based on the specific number of years mentioned in each part.