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Matilda wants to have $50,000 available in 8 years for future repairs on her home.  How much should she deposit into an account that yields 2.25% interest compounded monthly in order to have that amount?

User Alexmelyon
by
8.2k points

2 Answers

4 votes

Answer:

$41,770.55

Explanation:

Compound Interest Formula


\large \text{$ \sf A=P\left(1+(r)/(n)\right)^(nt) $}

where:

  • A = Final amount.
  • P = Principal amount.
  • r = Interest rate (in decimal form).
  • n = Number of times interest is applied per year.
  • t = Time (in years).

Given values:

  • A = $50,000
  • r = 2.25% = 0.0225
  • n = 12 (monthly)
  • t = 8 years

Substitute the given values into the formula and solve for P:


\implies \sf 50000=P\left(1+(0.0225)/(12)\right)^(12 \cdot 8)


\implies \sf 50000=P\left(1+0.001875}\right)^(96)


\implies \sf 50000=P\left(1.001875}\right)^(96)


\implies \sf P=(50000)/(\left(1.001875)\right)^(96)}


\implies \sf P=(50000)/(1.19701560...)


\implies \sf P=41770.55

Therefore, Matilda should deposit $41,770.55.

User Harsha Pokkalla
by
8.1k points
3 votes

Answer:

  • $41771.09

Explanation:

Given

  • Time t = 8 years,
  • Interest rate r = 2.25% = 0.0225,
  • Number of compounds n = 12 per year,
  • Final amount F = $50000.

To find

  • Amount of deposit P = ?

Solution

Use the compound equation:


  • F=P(1+r/n)^(nt)

Plug in the values and solve for P:


  • 50000=P(1+0.0225/12)^(8*12)

  • 50000=P(1+0.0225/12)^(96)

  • 50000=1.197P

  • P=50000/1.197

  • P=41771.09

User Aggressionexp
by
8.2k points

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