Financial Math
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Real financial math questions asked by students, solved step by step Every question below was submitted by a real student and answered step by step.
After five years the balance is 1,660.84 dollars. Use A = Pe^(rt) with rt = 0.065 times 5 = 0.325, and keep e^0.325 unrounded until the final cent.
The monthly deposit is $284.43, so Kevin pays in $54,610.56 and interest contributes $20,389.44. The accumulation factor is 1.83499060 over 192 months.
The monthly deposit is $297.11, so James pays in $60,610.44 and interest supplies $24,389.56. Solve the ordinary-annuity future-value formula for PMT first.
Answer: r = 0.0015341, about 0.1534% per period. Total payments of 121.20 against a principal of 120 leave only 1.20 of interest, so the rate must be tiny.
Reach a $85,000 future value in 17 years at 3.8% APR compounded monthly. Find the monthly deposit, the total paid in, and the interest earned — full step-by-step solution.
The account holds 2,910.89 dollars. Apply A = Pe^(rt) with rt = 0.04 times 7 = 0.28, and keep e^0.28 = 1.32312981 unrounded until the final cent.
The yield to maturity is 10.52%. See how to solve 938 = 80/(1+y) + 80/(1+y)^2 + 1080/(1+y)^3 by bracketing the root and refining it numerically.
a ≈ 1.6823. Collect the a terms — 450 − 240 − 58.5 + 15 = 166.5 — and the constants — −280.1 — so the break-even point is simply 280.1 divided by 166.5.
The answer is x = 212,378,875/91,944 ≈ 2,309.872. The 5% commission on the left side moves 0.05 × 25.92 = 1.296 to the right, leaving 849,515.5 = 367.776x.
An account compounded annually grows from $4,400 to $5,790 in 5 years, so the rate is (5790/4400)^(1/5) − 1 = 5.6444%, which rounds to 5.6% — not 5.7%.
The answer is 139.6125. This is the simple-interest product P*r*t with a daily rate scaled over 365 days, and the decimals give exactly four places.
A 3300 dollar loan at 5% compounded continuously grows to 3834.05 after three years, using A = Pe^(rt) with rt = 0.15 and e^0.15 = 1.1618342427.
Metre prices form an AP: 80,000 dong first, +5,000 each metre, so the 50th metre costs 325,000. The 50-metre total is (50/2)(80,000 + 325,000) = 10,125,000 dong.
x ≈ 1,546,839,575.67. Drop the matching percent signs, so −0.0675129744 = −104,431,740.75 / x, and divide the loss by the rate to recover the base.
x ≈ 1,467,474,033.32. Here the left side is already a decimal ratio, so x is the loss divided by that ratio — about 79 million less than in the percent-form variant.
The account reaches $6,888.98 after 96 deposits. Celine puts in $5,760 of her own money, so compounding adds $1,128.98 over the eight years.
Regular hours pay 40 x 95 = 3,800 and the 6 overtime hours pay 125 percent, or 118.75 each, for 712.50 - a total of 4,512.50 pesos.
Save $60 every month for 8 years in an account earning 4.4% APR compounded monthly. Work out the final balance with the annuity future value formula, step by step.
The result is 0.0972978C, a rise of 9.72978%. The two increases multiply to 1.0972978 rather than adding to 9.51%, because the second applies to the grown amount.
The principal is about $1,555.00. Divide 5,800 by the 240-period growth factor (1.0055)^240 = 3.72991; the often-quoted 3.6521 is wrong and inflates it.
The land is worth about 386,614,195 baht. Count 121 days between the dates, use t = 121/365 in V = P(1 + r)^t, and keep the growth factor to full precision.
Deposit $700 every quarter for 20 years at 7.2% APR compounded quarterly. Separate the future value into money paid in and interest earned, step by step.
Answer: 2290.05. Apply A = P(1 + r/n)^(nt) with P = 2000, r/n = 0.0085 and nt = 16 quarters, giving a growth factor of 1.0085^16 = 1.14502361.
The account grows to $123,160.64. Mia deposits $56,000 of her own money and interest supplies $67,160.64 — more than half the final balance.
The answer is $12,415.48. With r/n = 0.076 and nt = 6 periods, A = 8000(1.076)⁶, so the period rate is half the annual rate and the exponent doubles.
Answer: x = 0.01146052, about 1.1461% per period. Take the 10th root of 1.1207 via logarithms to get 1.01146052, then subtract 1 and compound back to check.
Answer: x = 0 and x = -0.01508489. Move the 1 across, note the trivial root, then bracket the second root by sign change; the curve dips to -0.00348 near x = -0.00745.
Answer: x = 0.00201143, about 0.2011% per period. Take the 15th root of 1.0306 with logarithms, subtract 1, and verify by raising the factor to the 15th power.
Answer: x = 0.00571394, about 0.5714% per period. Take the 20th root of 1.1207 to get 1.00571394, subtract 1, and check by raising the result back to the 20th power.
The answer is x = 1,501,376,500/19,154,163 ≈ 78.3838. Collecting the three x-rates gives 37,460.09x, and the 30% share moves 11,238.027x across.
The answer is x = 9,050,000/87 ≈ 104,022.99. The 13% term contributes −156x, flipping the left coefficient negative, so the two sides meet at 1343.28x = 139,732,000.
The answer is x = 290.50. Factoring x out gives the multiplier 1 + 0.0152/0.9848 = 1.015435, so the net is the adjusted total divided by that figure.
The net amount is x = 3,143.82. Factor x out of the two terms that contain it: the coefficient 1 + 0.019/0.981 = 1.019368 is the gross-up multiplier.
The answer is x = 7,100,000/27 ≈ 262,962.96. Because x sits inside the bracket, the equation is self-referential: expanding gives x = 284,000 − 0.08x, so 1.08x = 284,000.
The answer is x = 3,550,000/11 ≈ 322,727.27. Collecting the constants gives x = 355,000 − 0.10x, so 1.10x = 355,000 with no outer discount applied.
You would receive $47.40. Multiply the per-share dividend $0.79 by the 60 shares held, then round the product to the nearest cent to get the cash payout.