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RV-10-001 · Compound growth followed by a fixed withdrawal

An account starts with £5600. It earns 6% compound interest each year. After 4 years, £300 is withdrawn. Interest is credited before the withdrawal.

(a) Work out the balance immediately after the withdrawal. Give your answer to the nearest penny.

(b) The remaining balance is left for one further year at the same rate. Will it reach £6200? Show a calculation.

Part (a) Compound Percentages with Fixed Withdrawal Booklet p. 52
Method
1) Apply Original × ((100 + %)/100)^Time then subtract withdrawal
2) Multiply unrounded remaining balance by annual multiplier and compare with target
Worked Example (RV-10-001 · Part (a))
Work out the balance immediately after the withdrawal. Give your answer to the nearest penny.
Booklet p. 51–52: Original Amount×(100±%100)Time=New Amount\mathbf{\text{Original Amount} \times \left(\frac{100 \pm \%}{100}\right)^{\text{Time}} = \text{New Amount}}
1) Use multiplier 1.06.
2) 5600(1.06)4−3005600(1.06)^4-300
3) £6769.87
£6769.87
Part (b) Compound Percentages with Fixed Withdrawal Booklet p. 52
Method
1) Apply Original × ((100 + %)/100)^Time then subtract withdrawal
2) Multiply unrounded remaining balance by annual multiplier and compare with target
Worked Example (RV-10-001 · Part (b))
The remaining balance is left for one further year at the same rate. Will it reach £6200? Show a calculation.
Booklet p. 51–52: Original Amount×(100±%100)Time=New Amount\mathbf{\text{Original Amount} \times \left(\frac{100 \pm \%}{100}\right)^{\text{Time}} = \text{New Amount}}
1) Multiply the unrounded balance by the annual multiplier.
2) £7176.06
3) Compare this amount with the target.
£7176.06; yes.