Question

What is the future value of the 10% savings from earnings of $187.45 if it earns 5% annual interest, compounded monthly for 30 years? Use the compound interest formula to estimate the present value

Answer 1

I need one quick clarification: is the $187.45 an amount earned per month (so 10% = $18.745 saved each month), or is it a one‑time amount with 10% (= $18.745) invested today? I’ll give both common interpretations.

Inputs used
- 10% of $187.45 = $18.745 (≈ $18.75)
- annual rate r = 5% = 0.05
- compounding monthly: m = 12
- time t = 30 years → n = m·t = 360
- monthly rate i = r/m = 0.05/12 ≈ 0.0041666667

1) If $18.745 is a one‑time (lump) deposit now:
- FV = P(1 + i)^n = 18.745*(1.0041666667)^360 ≈ 18.745 * 4.467744 ≈ $83.75

(And the present value of that FV discounted back at the same rate is just the original $18.745.)

2) If $18.745 is saved every month (an ordinary monthly annuity):
- FV = PMT * [((1 + i)^n − 1) / i]
- (1 + i)^n ≈ 4.467744, so ((1+i)^n − 1)/i ≈ 3.467744 / 0.0041666667 ≈ 832.25856
- FV ≈ 18.745 * 832.25856 ≈ $15,600.69

- Present value of that 30‑year monthly stream at 5% (monthly) is
PV = PMT * [1 − (1 + i)^−n] / i ≈ 18.745 * 186.30144 ≈ $3,492.22

If you confirm the savings frequency (one‑time vs monthly), I can keep only the relevant result or show more decimals.