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please I need help to solve this (1) Suppose money grows according to the simple

ID: 3194834 • Letter: P

Question

please I need help to solve this

(1) Suppose money grows according to the simple interest accumulation function (t) 1 + .05. How much money would you need to invest at time 3 in order to have $3,200 at time 8? (2) Find the value at 1 = 6 of $4,850 to be paid at time 12 if a(t) = (1-041)' (3) Frances Morgan purchased a house for $156,000 on July 31, 2002. If real estate prices rose at a compound rate of 6.5% annually, how much was the home Frances bought worth on July 31, 1998? (4) A payment of $X two years from now along with a payment of $2X four years from now repays a debt of $6,000 at 6.5% annual effective compound interest. Find X (5) What is the present value of $5,000 due in ten years assuming money grows according to compound interest and the annual effective rate of interest is 4% for the first three years, 5% for the next two years, and 5.5% for the final five years? (6) Show that if the growth of money is governed by compound interest at an annual effective interest rate i > 0, then the sum of the current value of a payment of SK made n periods ago and a payment of SK to be made n periods from now is greater than $2K. More generally, what must be true about the operative accumulation function a(t) in order that the stated conclusion holds? (7) You have two options to repay a loan. You can repay $6,000 now and $5,940 in one year, or you can repay $12,000 in 6 months. Find the annual effective interest rate(s) i at which both options have the same present value.

Explanation / Answer

Solution 1:

for time 3: a(3) = 1 + 0.05(3) = 1.15

for time 8: a(8) = 1 + 0.05(8) = 1.40

3200/a(8) = 3200/1.4

This is the amount deposited at t = 0, so now we have to use this to find the amount that would be needed at t = 3 instead.

3200*(a(3))/1.4

3200*(1.15)/1.4 = $2, 628.57

Thus the amount needed to deposit at t = 3 in order to grow to $3200 at t = 8 is $2,628.57