Question

Please indicate all steps taken to solve this question clearly so it is easy to understand. Thank you.

Problem #7: You deposit P dollars into an account that earns a nominal rate of compounded semiannually. At the same time, you deposit 1.8P dollars into an account that earns simple interest at an annual rate of i. If both deposits earn the same amount of interest in the last 6 months of year 7, what is i? Answer as a percentage, correct to 2 decimals. Problem #7: 21.92 Just Save Your work has been saved! (Backt Admin Page) Submit Problem #7 for Grading Problem #7| Attempt #1 Your Answer:21.92 Attempt #2 Attempt #3 | Attempt #4 Attempt #5 Your Mark: 0/2x

Answer 1

Assume P=1

By trial and error

Interest assumption
1	15%
Period	0	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5	5.5	6	6.5	7
1P Interest	0.000	0.150	0.173	0.198	0.228	0.262	0.302	0.347	0.399	0.459	0.528	0.607	0.698	0.803	0.923
1P Principal	1.000	1.000	1.150	1.323	1.521	1.749	2.011	2.313	2.660	3.059	3.518	4.046	4.652	5.350	6.153
1.8P Interest	0.000		0.270		0.311		0.357		0.411		0.472		0.543		0.625
1.8P Principal	1.800		1.800		2.070		2.381		2.738		3.148		3.620		4.164
Interest assumption
2	20%
Period	0	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5	5.5	6	6.5	7
1P Interest	0.000	0.200	0.240	0.288	0.346	0.415	0.498	0.597	0.717	0.860	1.032	1.238	1.486	1.783	2.140
1P Principal	1.000	1.000	1.200	1.440	1.728	2.074	2.488	2.986	3.583	4.300	5.160	6.192	7.430	8.916	10.699
1.8P Interest	0.000		0.360		0.432		0.518		0.622		0.746		0.896		1.075
1.8P Principal	1.800		1.800		2.160		2.592		3.110		3.732		4.479		5.375
Interest assumption
3	10%
Period	0	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5	5.5	6	6.5	7
1P Interest	0.000	0.100	0.110	0.121	0.133	0.146	0.161	0.177	0.195	0.214	0.236	0.259	0.285	0.314	0.345
1P Principal	1.000	1.000	1.100	1.210	1.331	1.464	1.611	1.772	1.949	2.144	2.358	2.594	2.853	3.138	3.452
1.8P Interest	0.000		0.180		0.198		0.218		0.240		0.264		0.290		0.319
1.8P Principal	1.800		1.800		1.980		2.178		2.396		2.635		2.899		3.189
Interest assumption
4	8.80%
Period	0	0.5	1	1.5	2	2.5	3	3.5	4	4.5	5	5.5	6	6.5	7
1P Interest	0.000	0.088	0.096	0.104	0.113	0.123	0.134	0.146	0.159	0.173	0.188	0.205	0.223	0.242	0.263
1P Principal	1.000	1.000	1.088	1.184	1.288	1.401	1.525	1.659	1.805	1.964	2.136	2.324	2.529	2.751	2.993
1.8P Interest	0.000		0.158		0.172		0.188		0.204		0.222		0.241		0.263
1.8P Principal	1.800		1.800		1.958		2.131		2.318		2.522		2.744		2.986

Hence, answer is 8.80%

We could have also achieved this result by solving the following equation-

P*(1+i/2)^14-P*(1+i/2)^13 = 1.8P*(1+i)^7-1.8P*(1+i)^6

However, the above equation required more effort by trial and error or requires a solver function in excel