Question

You will deposit $10,000 into an account at the beginning of each year for 10 years. This account earns 10% simple interest per year, payable at the end of the year. Any interest earned in the account will be deposited into a second account. This account pays 5% interest, compounded semi-annually for the first 5 years, and pays a constant force of interest of 5% for the second 5 years. What is the total accumulated value in both accounts at the end of the 10 years?

Answer 1

It will be easier to calculate individual present vaue of payment rather then annuity.
The accumulated value of First account will be the total amount deposited because the interest amount is withdrawn at the end of every withdrawl.

Second Account Infbut Yoob 7000 koo8T 8 cool Sool 2opo 3 poo o 2 3 6 7 9 @ 5% compounds Semi connuelly 5% fore of interest .(2) = 2.5% 2 2 (+ 2) = (1+4") i = 1:025² -1 = 5.063% ha effective

Accumulated Vaka in First account loooo A sum of all deposits 10ooo tloooo lox 10ooo $1ooooo Accumulated Value in Second Account Valuat 5 year for first Spayments is - Vat s your > 1000 (1.0506)* + 2003.11.0506) + 3000 (1. osos + 4000 (1.0506) + 5000 1218.29 +2319.22+ 3311-28+4202.4 + sooo = $16051.19 Value at 5 year for last 5 payments is - -oos -005x2 Value at syear + = 6000 e + 7000 et 8000 e -oosxY + 9000 e -0.058S 10000 5707:38+ 6333.86 + 6885.66 + 7368.58 + 7788 = $34083.48 Total Value at Syear = 16051-19+34083.48= $501 34-67

Page No. 0-05X5 Accumulated value of second Account = 50134.67 e = $64374-19 Total Accumulated Value = 10000 +64374.19 =$164374-19