Question: Suppose you had a lump sum of £50,000 to invest in an annuity that will pay a monthly income for 10 years. If the issuing insurance company uses a nominal interest rate of 7% p.a compounded monthly, how much would your monthly income be?
My approach:
I found the effective yearly interest using the following formula:
((1+(i/n))^n)-1 => ((1+(0.07/12)^12)-1 => 0.07229 = ~7.23%
So I worked out the future value of £50,000 in 10 years time at an effective interest rate of 7.23% => £50,000(1.0723)^10 = £100,492.36
From this point, I divided by the number of time periods in question (Monthly payments*no. of years) => 12*10 = 120
£100,492.36/120 = £837.44 = Monthly Income
Is this the right way to go about this question, and is my solution correct?