Today is January 1.Starting today, Sam is going to contribute £140 on the ﬁrst of each month to his retirement account.His employer contributes an additional 50% of the amount contributed by Sam. If both Sam and his employer continue to do this and Sam can earn a monthly rate of ½ of 1 percent, How much will he have in his retirement account 35 years from now?

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Quizplus · Accepted Answer

Sam contributes £140 monthly, and his employer adds an additional 50% of Sam's contribution, which is £70. Therefore, the total monthly contribution is £210. The monthly interest rate is 0.5%. To find the future value of this annuity, we use the future value of an annuity formula: $FV = P \times \frac{(1 + r)^n - 1}{r}$, where P is the total monthly contribution, r is the monthly interest rate, and n is the total number of contributions. Here, $P = £210$, $r = 0.005$ (0.5%), and $n = 35 \times 12 = 420$ months. Plugging these values into the formula gives the future value of Sam's retirement account, which is closest to the value given in option E, £300,685.11.

Today Is January 1