Level 2 · Save for it, or borrow and repay?

Future value: what regular savings grow to

If you put the same amount aside at the end of every month and the account pays a monthly rate r, after n months you have:

fv = saving * ((1 + r) ** n - 1) / r

Each deposit earns interest for the months it sits in the account: the first one for 35 months, the last one for none. The formula adds all of that up in one step. In Excel it is =FV(4%/12, 36, -9584.05); the deposit is negative because it leaves your hands, and the result comes back positive.

Sizing it from the store’s own numbers

A savings plan pegged to revenue should use real revenue. Harbor & Pine’s completed revenue in 2025 averaged $191,680.90 a month, ranging from $99,903 in February to about $290,000 in November and December:

monthly_revenue.mean()             # 191680.90
round(0.05 * monthly_revenue.mean(), 2)   # 9584.05 a month

The answer assumes 2025 is a typical year and that the 5% is transferred every month even in a slow February. Write both assumptions down; a finance lead will ask.

Months to repay: NPER

The reverse question: given a payment, how many months does a loan take? Solve the loan formula for n:

r = 0.075 / 12
n = -math.log(1 - 48_000 * r / 1_500) / math.log(1 + r)    # 35.81
math.ceil(n)                                                # 36 payments

The answer is rarely a whole number: 35.81 means 35 full payments and a smaller 36th. Report it rounded up. Excel’s =NPER(7.5%/12, -1500, 48000) gives the same 35.81. If the payment is too small to cover even the first month’s interest ($48,000 × r = $300 here), the logarithm has no answer: the loan would never be repaid.

Common mistakes

• Annual rate, monthly periods. (1.04) ** 36 compounds 4% thirty-six times and returns $743,706 instead of $365,934.
• Rounding months down. 35 payments of $1,500 leave money owed; the loan needs a 36th.
• Forgetting interest exists. 36 × $9,584.05 = $345,025.80 is what you paid in, not what the account holds.
• Projecting from one good month. Use an average over a full year, so the holiday peak doesn’t set the plan.