You make semiannual withdrawals from an account starting in month 6 for $500 and increasing by...

You make semiannual withdrawals from an account starting in month 6 for $500 and increasing by $100 each semiannual period thereafter until end of year 4. The account pays 12% compounded monthly (calculate and write in the test the exact effective interest rate up to 4 decimals. How much should you deposit into the account now if you want to have a balance in the account of $1500 immediately after the last withdrawal (end of year 4)?

Expert Solution

i = 12% / 12 = 1% per month

Effective interest rate per semiannual period = (1+0.01)^6 - 1

= (1.01)^6 - 1

= 0.061520151 ~ 6.1520% (Four decimal places)

t = 4*2 = 8 semiannual periods

Amount to be deposited = 500*(P/A,6.1520%,8) + 100*(P/G,6.1520%,8) + 1500*(P/F,6.1520%,8)

= 500*(((1 + 0.061520)^8-1)/(0.061520*(1 + 0.061520)^8)) + 100*(((1 + 0.061520)^8-1)/((0.061520^2)(1 + 0.061520)^8) - 8/(0.061520*((1 + 0.061520)^8))) + 1500*((1 + 0.061520)^-8)

= 500*(((1.061520)^8-1)/(0.061520*(1.061520)^8)) + 100*(((1.061520)^8-1)/((0.061520^2)(1.061520)^8) - 8/(0.061520*((1.061520)^8))) + 1500*((1.061520)^-8)

= 500*6.172609 + 100*19.6768551 + 1500*0.620261

= 5984.38

Rahul Sunny answered 2 years ago

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