Q: Gian Carlo invests $58000 and receives and annuity of $7000 at the end of each year for thirteen yrs. Each time Gian Carlo gets a $7000 payment, he immediately deposits $4000 in a savings account that earns 9%. Find the annual yield recerived by Gian Carlo.
My solution is as follows:
Using financial calculator. let PV=-58000 PMT=7000 FV=0 N=13 find I/Y=7.91372%
Then find the FV of the savings account: let PV=0 PMT=-4000 N=13 and I/Y=9% find FV=91813.53832
7000-4000=3000 that Gian Carlo receives that is not accumulating any interest. So at the end of the 13yrs it should accumulated to 3000*13 = 39000
So the total amount of money Gian Carlo receives at the end of 13yrs is 39000+91813.53832 = 130813.5383 and the initial investment is 58000
Therefore, 58000 (1+i)^13 = 130813.5383 i=0.06456 = 6.456%
But the correct answer is 7.9020% and they used PV=-58000 N=13 PMT=3000 and FV=91813.54 to find I/Y.
I understand that they look at the 3000 as the payment from the savings account each year. But I don't understand what's wrong with my way of looking at the question.
Thanks.
My solution is as follows:
Using financial calculator. let PV=-58000 PMT=7000 FV=0 N=13 find I/Y=7.91372%
Then find the FV of the savings account: let PV=0 PMT=-4000 N=13 and I/Y=9% find FV=91813.53832
7000-4000=3000 that Gian Carlo receives that is not accumulating any interest. So at the end of the 13yrs it should accumulated to 3000*13 = 39000
So the total amount of money Gian Carlo receives at the end of 13yrs is 39000+91813.53832 = 130813.5383 and the initial investment is 58000
Therefore, 58000 (1+i)^13 = 130813.5383 i=0.06456 = 6.456%
But the correct answer is 7.9020% and they used PV=-58000 N=13 PMT=3000 and FV=91813.54 to find I/Y.
I understand that they look at the 3000 as the payment from the savings account each year. But I don't understand what's wrong with my way of looking at the question.
Thanks.