Question

Assume that Serena Williams desires to accumulate $850,000 in 14 years using her money market fund balance of $197,196. At what interest rate must Serena’s investment compound annually? (Round answer to 0 decimal places, e.g. 5%.)

Answer 1

• All working forms part of the answer
• Present Value is $ 197,196.

At, ‘n’ rate of Interest compounded annually, $ 197,196 will become $ 850,000

• $ 850,000 = ($ 197,196 / Present Value factor of interest rate for 14^th year)

Present Value factor of interest rate for 14^th year = 197196 / 850000 = 0.231995….

• This Present Value factor of interest rate for 14^th year of 0.231995…. can be looked in the Factor table to see under which interest rate this figure is falling.
• Sample Factor table for different interest rate:

Year	5%	10%	11%
1	0.952380952	0.909090909	0.900900901
2	0.907029478	0.826446281	0.811622433
3	0.863837599	0.751314801	0.731191381
4	0.822702475	0.683013455	0.658730974
5	0.783526166	0.620921323	0.593451328
6	0.746215397	0.56447393	0.534640836
7	0.71068133	0.513158118	0.481658411
8	0.676839362	0.46650738	0.433926496
9	0.644608916	0.424097618	0.390924771
10	0.613913254	0.385543289	0.352184479
11	0.584679289	0.350493899	0.317283314
12	0.556837418	0.318630818	0.285840824
13	0.530321351	0.28966438	0.257514256
14	0.505067953	0.263331254	0.231994825

• It can be seen that at 14^th year, under 11% Interest rate, the value 0.231994825 is very close to the value computed by us above.
• Hence, Interest rate required = 11%