Mary wants to help pay for her granddaughter Beth\'s education. She has decided
ID: 2733812 • Letter: M
Question
Mary wants to help pay for her granddaughter Beth's education. She has decided to pay for half of the tuition costs at State University, which are now $11,000 per year. Tuituin is expected to increase at a rate of 7% per year into the forseeable future. Beth just had her 12th birthday. Beth plans to start college on her 18th birthday and finish in four years. Mary will make a deposit today and continue making deposits each year until Beth starts college. The account will earn 4% interest, compounded annually. How much must Mary's deposits be each year in order to pay half of Beth's tuition at the beginning of each school year?
Explanation / Answer
Calculation of Future Value of Money at the end of 18th Year
Year (a)
Years Remaining (b)
Money Required [ 5500 x (1+i)n ]
( c )
Present Value of All future Money at the end of 18 thYear
12Th
0
-
13th
1
-
14th
2
-
15th
3
-
16th
4
-
17th
5
-
18th
6
8254.02
8254.02 ( C x 1)
19th
7
8831.80
8492.11 ( C x 1.04 -1 )
20th
8
9450.02
8737.08 ( C x 1.04 -2 )
21st
9
10,111.53
8989.11 ( C x 1.04 -3 )
34,472.32
Amount required at the end of 18th year is $ 34,472.32
Interest rate = 4 %
Future Value of Money = $ 34,472.32
34,472.32 = R /0.04 [ (1.04 n+1 -1 ] – R
Where R = Regular annual payment, n = 6 year
34472.32 = R /0.04 [ (1.04 7 -1 ] – R
34,472.32 = 7.8983 R – R
R = $ 4,997.22
Answer- Regular annual payment of $ 4,997.22
Year (a)
Years Remaining (b)
Money Required [ 5500 x (1+i)n ]
( c )
Present Value of All future Money at the end of 18 thYear
12Th
0
-
13th
1
-
14th
2
-
15th
3
-
16th
4
-
17th
5
-
18th
6
8254.02
8254.02 ( C x 1)
19th
7
8831.80
8492.11 ( C x 1.04 -1 )
20th
8
9450.02
8737.08 ( C x 1.04 -2 )
21st
9
10,111.53
8989.11 ( C x 1.04 -3 )
34,472.32