An investment opportunity has the following characteristics

An investment opportunity has the following characteristics. You deposit 10000 into an account A at the end of each year for 10 years. The account earns an annual rate of 8%. at the end of each year, the interest in this account is paid to you and the interest is then reinvested in another account B which earns an annual rate of 5%. Determine your total accumulated value (in both accounts) after 10 years. A. 140,250 B. 142,250 C. 141,250 D. 143,250 E. 144,250

Solution

Depositing 10000 into an account A at the end of each year for 10 years implies that the interest will start getting paid from the end of the 2^nd year which will continue till the end of the 10^th year. The 1^st amount of interest is 1000*8/100 = 800.Since 10000 is deposited at the end of every year, the interests paid at the end of 2^nd, 3^rd, 4^th, …10^th year are 800*1, 800*2, 800*3,… 800*9 i.e. 800..,1600,2400,…,7200. The sum of these amounts is 9/2(800 +7200) = 9/2(8000) = 36000.

The interest received from account A is deposited in the account B which earns an annual rate of 5%. These deposits start at the end of 2^nd year and continue till the end of the 9^th year. The amount deposited in the account B is 36000-7200 = 28800. The interest received at the end of the 3^rd year is 800*5/100= 40.The interest received at the end of 3^rd ,4^th, 5^th, …10^th years are 40*1, 40*2, 40*3,…, 40*8 i.e, 40, 80, 120,…, 320. The sum of these amounts is 8/2( 40+320) = 8/2(360) = 1440.

Then the total accumulated value is 10*10000+ 36000+1440 = 100000+37440 = 137440.

NOTE: All the given answers are incorrect as we deposit 10000 into an account A at the end of each year for 10 years and NOT at the beginning of the year.