FinanceCalc Pro — TVM Solver

Solve For

Loan Amount

Rate (%)

Term

Compounding

Payments/Year

Timing

Monthly Payment

$0.00

Compounding: Monthly · Payments: Monthly · End of period · Effective Annual Rate: 6.72%

Present Value (PV)

The current worth of a future sum or stream of payments, discounted at a given interest rate. For loans, PV is the principal borrowed. For investments, it is your initial deposit.

\[PV = \dfrac{FV}{(1+r)^n}\]

\[PV_{\text{annuity}} = PMT \times \dfrac{1-(1+r)^{-n}}{r}\]

Future Value (FV)

The projected value of an investment at a future date, assuming constant interest and compounding. Shows how money grows over time.

\[FV = PV \times \left(1+\dfrac{r}{n}\right)^{nt}\]

\[FV_{\text{deposits}} = PV(1+r)^n + PMT \times \dfrac{(1+r)^n-1}{r}\]

Payment (PMT)

The fixed amount paid or deposited each period. For loans, this amortizes the debt. For savings, it is your regular contribution toward a goal.

\[PMT = PV \times \dfrac{r(1+r)^n}{(1+r)^n-1}\]

Number of Periods (N)

The total count of payment or compounding intervals to pay off a loan or reach a target. For a 30-year monthly mortgage, N = 360.

\[N = \dfrac{\ln\left(\dfrac{PMT}{PMT - PV \cdot r}\right)}{\ln(1+r)}\]

Annual Percentage Rate (APR) & Yield (APY)

APR is the nominal yearly rate. APY (Effective Annual Rate) reflects true yearly return after compounding.

\[APY = \left(1+\dfrac{r}{n}\right)^n - 1\]

Under continuous compounding, APY approaches:

\[APY_{\text{cont}} = e^{r} - 1\]

Continuous Compounding

The theoretical limit as compounding frequency approaches infinity. Uses Euler's constant $e \approx 2.71828$, representing maximum possible growth.

\[FV = PV \times e^{rt}\]

\[\lim_{n\to\infty}\left(1+\dfrac{r}{n}\right)^n = e^r\]

Example: $1,000 at 10% for 1 year → Monthly: $1,104.71 · Daily: $1,105.16 · Continuous: $1,105.17

Amortization (Loans)

At period 0, the loan is disbursed — you receive the principal (PV), no payment due yet. At the end of period 1, interest is charged only on PV; your payment covers this interest first, with the remainder reducing principal. Each subsequent period, interest is charged on the prior ending balance.

\[\text{Interest}_k = \text{Balance}_{k-1} \times r\]

\[\text{Principal}_k = PMT - \text{Interest}_k\]

\[\text{Balance}_k = \text{Balance}_{k-1} - \text{Principal}_k\]

Growth Schedule (Savings)

At period 0, the initial deposit (PV) is made — no interest yet. At the end of period 1, interest is earned only on PV; then the first regular deposit is added. Each subsequent period, interest is earned on the prior ending balance before that period's deposit is added.