Part 1 1.Find the future value of the following annuity due. Assume that interes
ID: 1135448 • Letter: P
Question
Part 1
1.Find the future value of the following annuity due. Assume that interest is compounded annually, there are n payments of R dollars, and the interest rate is i. R=15,000; i = 0.04; n=5
2. Find the interest rate for a $5000 deposit accumulating to $6100.95 , compounded quarterly for 5 years.
Part 2
1. Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest. R= 400; 6.26% intrest compunded semiannually for 10 years.
2. Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest. R=15,000; 4.9% Interest compounded quarterly for 14 years.
Explanation / Answer
Part 1
1)
Future Value of Annuity Due = (1+i) * PV * [ {(1+i)n -1} / i ]
Here PV = 15000, i = 0.04 and n 5
FV = (1+0.04) * 15000 * [ {(1+0.04)5 - 1} / 0.04 ]
= 1.04 * 15000 * 5.41632256
= 84,494.63
2)
FV = PV (1+i)n
Here, FV = 6100.95, PV = 5000 and n = 5 * 4 = 20
6100.95 = 5000* (1+i) 20
1.22019 = (1+i)20
(1.22019)(1/20) = (1+i)
1.01 = 1+ i
0.01 = i
Therefore, Interest rate = 0.01 * 4 i.e 0.04 or 4% compounded quarterly
Part 2
Future Value of an ordinary annuity = R * [ {(1+i)n - 1} / i ]
1)
Here, R = 400 , i = 6.26% / 2 = 3.13% , n = 10*2 = 20
FV = 400 * [ {(1+0.0313)20 - 1} / 0.0313]
= 400 * 27.22854
= 10,891.41
Amount from Contributions = R * no. of times
= 400 * 20
= 8000
Amount from Interest = Total Amount - Amount from contributions
= 10,891.41 - 8000
=2,891.41
2)
Here, R = 15,000 , i = 4.9% / 4 = 1.225% , n = 14*4 = 56
FV = 15,000 * [ {(1+0.01225)56 - 1} / 0.01225]
= 15,000 * 79.79573
= 1,196,935.95
Amount from Contributions = R * no. of times
= 15000 * 56
= 840,000
Amount from Interest = Total Amount - Amount from contributions
= 1,196,935.95 - 840,000
= 356,935.95